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A fractal-fractional mathematical model for COVID-19 and tuberculosis using Atangana-Baleanu derivative
(Taylor & Francis Inc, 2024) Gunasekar, T.; Manikandan, S.; Suba, M.; Akguel, Ali
This study aims to develop a compartmental epidemiological model for the co-infection of COVID-19 and tuberculosis, incorporating a Holling type II treatment rate for individuals with tuberculosis, COVID-19, and dual infections while considering incomplete treatment in some TB cases. The model analysis examines the sub-models for COVID-19, TB, and the combined co-infection model. Using the fixed-point method, the research investigates the existence and uniqueness of solutions for the proposed model. It also explores a stability analysis to evaluate Ulam-Hyer's reliability. Furthermore, it discusses and validates Lagrange's interpolation polynomial through a specific case study to numerically compare different fractal and fractional orders.
A method for solving the generalized Camassa-Choi problem with the Mittag-Leffler function and temporal local derivative
(Elsevier, 2023) Hashemi, Mir Sajjad; Akguel, Ali; Hassan, Ahmed; Bayram, Mustafa
This paper focuses on a reduction technique to discover exact solutions for the generalized Camassa-Choi equation with temporal local M-derivative. The paper presents various types of exact solutions along with their corresponding first integrals. Furthermore, the interactions between the orders of alpha and beta in the M-derivative are taken into account and depicted graphically for the derived solutions. Remarkably, the paper demonstrates that in certain situations, exact solutions can be obtained for any value of n, which holds significant mathematical intrigue. The authors note that Nucci's reduction technique has not previously been employed for differential equations with M-derivative, to the best of their knowledge.
A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications
(Mdpi, 2022) Nadeem, Muhammad; Akguel, Ali; Guran, Liliana; Bota, Monica-Felicia
The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (AHITM), for the approximate solution of wave problems in multi-dimensional orders. The Aboodh integral transform (AIT) removes the restriction of variables in the recurrence relation, whereas the homotopy perturbation method (HPM) derives the successive iterations using the initial conditions. The convergence analysis is provided to study a wave equation with multiple dimensions. Some computational applications are considered to show the efficiency of this scheme. Graphical representation between the approximate and the exact solution predicts the high rate of convergence of this approach.
A novel simulation methodology of fractional order nuclear science model
(Wiley, 2017) Akguel, Ali; Khan, Yasir
In this paper, a novel simulation methodology based on the reproducing kernels is proposed for solving the fractional order integro-differential transport model for a nuclear reactor. The analysis carried out in this paper thus forms a crucial step in the process of development of fractional calculus as well as nuclear science models. The fractional derivative is described in the Captuo Riemann-Liouville sense. Results are presented graphically and in tabulated forms to study the efficiency and accuracy of method. The present scheme is very simple, effective, and appropriate for obtaining numerical simulation of nuclear science models. Copyright (c) 2017 John Wiley & Sons, Ltd.
A proceeding to numerical study of mathematical model of bioconvective Maxwell nanofluid flow through a porous stretching surface with nield/convective boundary constraints
(Nature Portfolio, 2024) Imran, Muhammad; Basit, Muhammad Abdul; Yasmin, Sumeira; Khan, Shan Ali; Elagan, S. K.; Akguel, Ali; Hassan, Ahmed M.
Nanofluids become significant in the mass and heat transfer models, especially in engineering problems. Current proceedings focused on the bioconvective Maxwell nanofluid flow passing through the permeable stretchable sheet contingent to nield boundary conditions involving effects of activation energy and thermal radiation. Various physical quantities are involved in this mechanism like magnetic field, thermophoresis, and Brownian motion. The main objective of the study is to report the heat and mass transport in the existence of motile microorganisms. In a mathematical perspective, this structured physical model is going to govern with the help of partial differential equations (PDEs). These governing PDEs are then converted into dimensionless ordinary differential equations form by utilizing appropriate similarity transformations. For numerical results, the shooting technique with 'bvp4c' built-in package of MATLAB was implemented. Computed results are then visualized graphically and discussed effects of involving physical variables on the nano-fluid flow profiles are comprehensively. From results, it has been concluded that the fluid flow velocity, temperature, concentration, and microorganism density profiles show escalation on increasing the numeric values of porosity, thermophoresis, buoyancy ratio, bioconvection Rayleigh, Peclet number parameters and decrement reported due to increasing the counts of Prandtl number, magnetic field, radiation, Brownian motion, Lewis number as evident from figures. The numerical outcomes observed by fixing the physical parameters as 0.1 < lambda < 3.0, 0.1 < M < 1.5, 0.1 < Nr < 6.0, 0.1 < Rb < 1.5, 0.1 < Nb < 6.0, 0.1 < Nt < 1.0, 2.0 < Pr < 2.9, 0.1 < Rd < 0.4 . Magnetic field and Brownian motion create retardation impact due to the liquid momentum. In tables, the numerical values of Skin friction, Nusselt number, Sherwood number, and microorganisms density number are presented and also comparison table of our computed results and already published results is included for the validation.
Activation energy impact on unsteady Bio-convection nanomaterial flow over porous surface
(Amer Inst Mathematical Sciences-Aims, 2022) Tahir, Madeeha; Naz, Ayesha; Imran, Muhammad; Waqas, Hasan; Akguel, Ali; Shanak, Hussein; Jarrar, Rabab
Nanofluid is an advanced technology to enhance heat transportation. Additionally, the thermal conductivity of nanofluids is high therefore, they are more useful for heat transportation. Evaluation of entropy generation has been a helpful technique for tackling improvements in thermal features because it provides information that cannot be obtained via energy analysis. For thermodynamic irreversibilities, a good approximation is the rate of entropy generation. As a result of a reduction of entropy production, energy transport infrastructure has become more efficient. This study aims to analyse the bioconvective flow of nanofluid flow through a stretching sheet in the occurence of gyrotactic motile microorganisms. A magnetised nanomaterial model with thermophoretic and Brownian diffusion properties is analysed. The impacts of activation energy, temperature dependent and exponential base heat source are investigated in this analysis. The entropy generation of the system is also observed for nanofluid flow. The mathematical model is developed as partial differential equations. The governing equations are reduced to a dimensionless system of ordinary differential equations by applying similarity transformations. The ODEs are tacked numerically with the aid of shooting scheme in commercial software MATLAB. For graphical and numerical results of flow controlling parameters versus subjective fields, the commercial software MATLAB tool bvp4 is used with the shooting scheme. The novelty of this analysis computes numerical computation of bioconvective nanofluid flow with temperature -dependent and exponential base heat source investigated. Furthermore, the consequence of thermal radiation and entropy of the system is considered. The porous medium with activation energy is also taken into consideration. The results show that the velocity field is reduced with increased bioconvection Rayleigh number. The thermal field is increased via an exponential space -based heat source. The concentration is reduced via Lewis number. the microorganisms profile declines for larger bioconvection Lewis number. The Brinkman number Br, magnetic and permeability characteristics all showed a rising trend when plotted against the entropy production rate.
An exact solution of heat and mass transfer analysis on hydrodynamic magneto nanofluid over an infinite inclined plate using Caputo fractional derivative model
(Amer Inst Mathematical Sciences-Aims, 2022) Kayalvizhi, J.; Kumar, A. G. Vijaya; Sene, Ndolane; Akguel, Ali; Inc, Mustafa; Abu-Zinadah, Hanaa; Abdel-Khalek, S.
This paper presents the problem modeled using Caputo fractional derivatives with an accurate study of the MHD unsteady flow of Nanofluid through an inclined plate with the mass diffusion effect in association with the energy equation. H2O is thought to be a base liquid with clay nanoparticles floating in it in a uniform way. Bousinessq's approach is used in the momentum equation for pressure gradient. The nondimensional fluid temperature, species concentration, and fluid transport are derived together with Jacob Fourier sine and Laplace transforms Techniques in terms of exponential decay function, whose inverse is computed further in terms of Mittag-Leffler function. The impact of various physical quantities interpreted with fractional order of the Caputo derivatives. The obtained temperature, transport, and species concentration profiles show behaviours for 0 < alpha <1 where alpha is the fractional parameter. Numerical calculations have been carried out for the rate of heat transmission and the Sherwood number is swotted to be put in the form of tables. The parameters for the magnetic field and the angle of inclination slow down the boundary layer of momentum. The distributions of velocity, temperature, and concentration expand more rapidly for higher values of the fractional parameter. Additionally, it is revealed that for the volume fraction of nanofluids, the concentration profiles behave in the opposite manner. The limiting case solutions also presented on flow field of governing model.
An Intelligent Platform for Software Component Mining and Retrieval
(Mdpi, 2023) Bibi, Nazia; Rana, Tauseef; Maqbool, Ayesha; Afzal, Farkhanda; Akguel, Ali; De la sen, Manuel
The development of robotic applications necessitates the availability of useful, adaptable, and accessible programming frameworks. Robotic, IoT, and sensor-based systems open up new possibilities for the development of innovative applications, taking advantage of existing and new technologies. Despite much progress, the development of these applications remains a complex, time-consuming, and demanding activity. Development of these applications requires wide utilization of software components. In this paper, we propose a platform that efficiently searches and recommends code components for reuse. To locate and rank the source code snippets, our approach uses a machine learning approach to train the schema. Our platform uses trained schema to rank code snippets in the top k results. This platform facilitates the process of reuse by recommending suitable components for a given query. The platform provides a user-friendly interface where developers can enter queries (specifications) for code search. The evaluation shows that our platform effectively ranks the source code snippets and outperforms existing baselines. A survey is also conducted to affirm the viability of the proposed methodology.
An investigation of (2+1)-dimensional asymmetric Nizhnik-Novikov-Veselov system: Lie symmetry reductions, invariant solutions, dynamical behaviors and conservation laws
(Elsevier, 2022) Kumar, Sachin; Kumar, Amit; Inc, Mustafa; Alotaibi, Hammad; Abdou, M. A.; Akguel, Ali
In this study, we develop the asymmetric Nizhnik-Novikov-Veselov (ANNV) system in (2+1)-dimensions, which has applications in processes of interaction of exponentially localized wave structures, as well as the infinitesimal generators, Lie symmetries, vector fields, and the commutator table. The link between Lie symmetry vectors and conserved vectors is constructed using symmetry conservation principles once Lie point symmetries are first deduced. Using the aforementioned Lie symmetry technique, two-stage symmetry reductions are used to obtain the precise analytical answers. These analytical solutions all incorporate a number of different functional parameters as well as arbitrary constant parameters. The diversity of the physical phenomena of the obtained soliton solutions is illustrated by the inclusion of arbitraryness of functional parameters and constants. By using Noether's method, conservation laws have subsequently been attained. The innovative aspect of the work described in this paper is an attempt to use 3-dimensional and 2-dimensional visuals, along with appropriate arbitrary parameter selections and functional parameter values, to represent the dynamical behavior of the solutions that have been produced. In order to make this research more intriguing, stripe solitons, dark-bright solitons, solitary waves, singular wave-form soliton, and other types of soliton wave profiles of the achieved solutions are described. The effectiveness, benefits, and utility of the employed approach are demonstrated by the physical and graphical interpretation of the answers attained.
Analysis and dynamical transmission of tuberculosis model with treatment effect by using fractional operator
(Taylor & Francis Inc, 2024) Farman, Muhammad; Mehmood Malik, Shahid; Akguel, Ali; Ghaffari, Abdul Sattar; Salamat, Nadeem
Each year, millions of people die from the airborne infectious illness tuberculosis (TB). Several drug-susceptible (DS) and drug-resistant (DR) forms of the causative agent, Mycobacterium tuberculosis (MTB), are currently common in the majority of affluent and developing nations, particularly in Bangladesh, and completely drug-resistant strains are beginning to arise. The main purpose of this research is to develop and examine a non-integer-order mathematical model for the dynamics of tuberculosis transmission using the fractal fractional operator. By demonstrating characteristics such as the boundedness of solutions, positivity, and reliance of the solution on the original data, the biological well-posedness of the mathematical model formulation was investigated for TB cases from 2002 to 2017 in KPK Pakistan. Ulam-Hyres stability is also used to assess both local and global aspects of TB bacterial infection. Sensitivity analysis of the TB model with therapy was also examined. The advanced numerical technique is used to find the solution of the fractional-order system to check the impact of fractional parameters. Simulation highlights that all classes have converging qualities and retain established positions with time, which shows the actual behavior of bacterial infection with TB.
Analysis of a diffusive chemical reaction model in three space dimensions
(Taylor & Francis Inc, 2024) Ahmed, Nauman; Ali, Javaid; Akguel, Ali; Hamed, Y. S.; Aljohani, A. F.; Rafiq, Muhammad; Khan, Ilyas
This article proposes an implicit operator splitting nonstandard finite difference (OS-NSFD) scheme for numerical treatment of two species in three space dimensions reaction-diffusion glycolysis model. Since, the unknown state variables exhibiting the concentrations of species in glycolysis models and they cannot be negative and obtaining their positive solutions is a challenging task. The established theoretical result ensures that our proposed OS-NSFD scheme is unconditionally convergent at equilibrium point and fulfills the condition of positivity of solutions on contrary to other methods. Further, we analyze the existence and uniqueness of the solution obtained for the underlying system. To highlight the effectiveness of OS-NSFD scheme we compare the simulation results of OS-NSFD scheme with three well-known existing operators splitting finite difference (FD) schemes, namely, forward Euler explicit, backward Euler implicit and Crank Nicolson splitting schemes. Many existing techniques provide with the restricted positive solutions which do not work always. These techniques are only applicable if certain conditions on the discretized parameters are considered otherwise; they produce negative solutions, which is not the physical feature of the real system. The current work bridges this gap by catering the unconditional positive solutions to the reaction diffusion models.
Analysis of some dynamical systems by combination of two different methods
(Nature Portfolio, 2024) Ganie, Abdul Hamid; Zidan, A. M.; Shah, Rasool; Akguel, Ali; Hassani, Murad Khan
In this study, we introduce a novel iterative method combined with the Elzaki transformation to address a system of partial differential equations involving the Caputo derivative. The Elzaki transformation, known for its effectiveness in solving differential equations, is incorporated into the proposed iterative approach to enhance its efficiency. The system of partial differential equations under consideration is characterized by the presence of Caputo derivatives, which capture fractional order dynamics. The developed method aims to provide accurate and efficient solutions to this complex mathematical system, contributing to the broader understanding of fractional calculus applications in the context of partial differential equations. Through numerical experiments and comparisons, we demonstrate the efficacy of the proposed Elzaki-transform-based iterative method in handling the intricate dynamics inherent in the given system. The study not only showcases the versatility of the Elzaki transformation but also highlights the potential of the developed iterative technique for addressing similar problems in various scientific and engineering domains.
Bifurcations, stability analysis and complex dynamics of Caputo fractal-fractional cancer model
(Pergamon-Elsevier Science Ltd, 2022) Xuan, Liu; Ahmad, Shabir; Ullah, Aman; Saifullah, Sayed; Akguel, Ali; Qu, Haidong
The association of cancer and immune cells has complex nature and produces chaotic behavior when it is simulated. The newly introduced operators which combine the fractal and fractional operators produce excellent and profound hidden attractors in a chaotic system which is sometimes not possible to get hidden attractors using integer order operators. The cancer model is considered under fractal fractional operator in Caputo sense. Linear stability of different equilibrium points is analyzed. The primary objective of the current paper is to analyze different bifurcations like pitch-fork, quasi, and inverse period-doubling bifurcations. Another important objective of this article is to study hidden limit cycle type chaotic structures of the cancer model via Caputo fractalfractional operator. The existence and uniqueness of the solution and Ulam-Hyres (UH) stability are studied through the concepts of nonlinear analysis. The numerical solution is derived through the predictor-corrector method. The obtained results were presented and validated through numerical simulations. The lyapunov spectra of the state variables are presented through graphical illustration and table. Sensitivity of the state variables to the initial conditions are simulated for initial conditions 0.1 and 0.11. For various values of fractal dimensions and fractional orders, the time series oscillations and hidden limit cycles type chaotic attractors are graphically presented through MATLAB-17.
Breather, lump, M-shape and other interaction for the Poisson-Nernst-Planck equation in biological membranes
(Springer, 2024) Ceesay, Baboucarr; Ahmed, Nauman; Baber, Muhammad Zafarullah; Akguel, Ali
This paper investigates a novel method for exploring soliton behavior in ion transport across biological membranes. This study uses the Hirota bilinear transformation technique together with the Poisson-Nernst-Planck equation. A thorough grasp of ion transport dynamics is crucial in many different scientific fields since biological membranes are important in controlling the movement of ions within cells. By extending the standard equation, the suggested methodology offers a more thorough framework for examining ion transport processes. We examine a variety of ion-acoustic wave structures using the Hirota bilinear transformation technique. The different forms of solitons are obtained including breather waves, lump waves, mixed-type waves, periodic cross-kink waves, M-shaped rational waves, M-shaped rational wave solutions with one kink, and M-shaped rational waves with two kinks. It is evident from these numerous wave shapes that ion transport inside biological membranes is highly relevant, and they provide important insights that may have an impact on various scientific disciplines, medication development, and other areas. This extensive approach helps scholars dig deeper into the complexity of ion transport, illuminating the complicated mechanisms driving this essential biological function. Additionally, to show the physical interpretations of these solutions we construct the 3D and their corresponding contour plots by choosing the different values of constants. So, these solutions give us the better physical behaviors.
Central composite design (CCD)-Response surface methodology (RSM) for modeling and simulation of MWCNT-water nanofluid inside hexagonal cavity: Application to electronic cooling
(Elsevier, 2023) Wang, Jianfeng; Khan, Shan Ali; Yasmin, Sumeira; Alam, Mohammad Mahtab; Liu, Haihu; Farooq, Umar; Akguel, Ali
Purpose: In application of hexagonal shapes, engineers and researchers use mathematical modeling, computational fluid dynamics (CFD), and experimental techniques to study natural convection inside hexagonal cavities and improve the design and efficiency of engineering systems. The exploration of fluid performance in hexagonal cavity has been an important problem from the earlier in the fluid mechanics field. The present transient study about thermal reaction and behavior of natural convectional MWCNT-water nanofluid flow privileged a hexagonal cavity in the occurrence of magnetic field is scrutinized. The flow domain of hexagonal structure cavity is a partitioned with lower heated cavity wall and inner four blocks are also heated. The upper wall of the cavity is considered insulated. Furthermore the other remaining walls of the hexagonal cavity are cold.Approach: The two-dimensional steady, incompressible, governing equations which involve continuity, velocity, and temperature equations of mono nanofluid in a dimensionless form are expressed in vertically and horizontal directions respectively. Moreover, transformed the governing equations into their dimensionless system then elucidated numerically with the help of Galerkin Finite Element Method. Furthermore response surface methodology (RSM) has been utilized to obtaining the optimal values of the designed parameters. This combined process was successfully sculpted and optimized utilized a central composite design with response surface methodology.Findings: The numerical fallouts of the flow controlling parameters scrutinized containing streamlines, velocities components and isotherms are elaborated. The investigation depicts enhanced convection velocity and temperature outcomes for different values of Rayleigh number. The average Nusselt number is drops as Rayleigh number boosts up. It is concluded that the Nusselt number is reduces for Hartmann number. For larger nanoparticles fraction Nusselt number increases.Limitations: This analysis has particular scope for improvement. In additions, studies can be showed on the improvement of hexagonal cavity walls designs, thickness, and size of the walls of enclosure cavity. Furthermore the heated blocks are involved inside the cavity.Practical application: The natural convection flow through hexagonal cavity reveals major importance and those geometrical shapes are playing major role in electronic cooling. In electronics, hexagonal cavities can be found in heat sinks and electronic packages. Natural convection plays a crucial role in dissipating heat from electronic devices, such as microprocessors, power electronics, and LED lighting systems. Nanofluids exhibit potential heat transfer as compared to conventional coolants. With this aim, the current analysis enlightens the natural convection flow of MWCNTs-water nanofluid inside hexagonal cavity and square-shaped blocks.Originality: This analysis is original, and no previous investigation has been accompanied considering the enclosure domain of cavity and variation of the walls number.
Coherent manipulation of giant birefringent Goos-Hänchen shifts by compton scattering using chiral atomic medium
(Nature Portfolio, 2024) Haq, Zia Ul; Ahmad, Iftikhar; Bacha, Bakht Amin; Akguel, Ali; Hassani, Murad Khan
A four level chiral medium is considered to analyze and investigate theoretically the reflection/transmission coefficients of right circularly polarized (RCP) beam and left circularly polarized (LCP) beam as well as their corresponding GH-shifts under the effect of compton scattering. Density matrix formalism is used for calculation of electric and magnetic probe fields coherence. The polarization and magnetization are calculated from probes coherence terms in the chiral medium. The electric and magnetic susceptibilities as well as chiral coefficients are related with polarization and magnetization. The refractive indices of RCP and LCP beams under compton scattering effect is modified from the electric/magnetic susceptibilities, chiral coefficients, mass and charge of electron as well as compton scattering angle. The giant positive and negative birefringent Goos-H & auml;nchen (GH) shifts in reflection and transmission beams are investigated in this manuscript under Compton scattering effect. The RCP and LCP beams obey the normalization condition |R(+,-)|+|T(+,-)|=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|R<^>{(+,-)}|+|T<^>{(+,-)}|=1$$\end{document} at the interface of a lossy chiral medium of |A(+,-)|similar or equal to 0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|A<^>{(+,-)}|\simeq 0$$\end{document} and a thin sheet of balsa wood under the effect of compton scattering angle, incident angle, probe field detuning, control field Rabi frequency, phases of electric and magnetic fields and phase of superposition states. Significant positive/negative giant GH-shifts in reflection and transmission beams are investigated. The results show potential applications in modification of cloaking devices, image coding, polarizing filters and LCD displays.
Comparative study of ternary hybrid nanofluids with role of thermal radiation and Cattaneo-Christov heat flux between double rotating disks
(Nature Portfolio, 2023) Noreen, Sobia; Farooq, Umar; Waqas, Hassan; Fatima, Nahid; Alqurashi, M. S.; Imran, Muhammad; Akguel, Ali
Heat and mass transfer are crucial to numerous technical and commercial operations, including air conditioning, machinery power collectors, crop damage, processing food, heat transfer mechanisms, and cooling, among numerous others. The fundamental purpose of this research is to use the Cattaneo-Christov heat flux model to disclose an MHD flow of ternary hybrid nanofluid through double discs. The results of a heat source and a magnetic field are therefore included in a system of PDEs that model the occurrences. These are transformed into an ODE system using similarity replacements. The first-order differential equations that emerge are then handled using the computational technique Bvp4c shooting scheme. The Bvp4c function in MATLAB is used to numerically solve the governing equations. The influence of the key important factors on velocity, temperature, nanoparticles concentration, and is illustrated visually. Furthermore, increasing the volume fraction of nanoparticles improves thermal conduction, increasing the heat transfer rate at the top disc. The graph indicates that a slight increase in melting parameter rapidly declines the velocity distribution profile of nanofluid. The temperature profile was boosted due to the growing outcomes of the Prandtl number. The increasing variations of the thermal relaxation parameter decline the thermal distribution profile. Furthermore, for some exceptional instances, the obtained numerical answers were compared to previously disclosed data, yielding a satisfactory compromise. We believe that this discovery will have far-reaching ramifications in engineering, medicine, and the field of biomedical technology. Additionally, this model can be used to examine biological mechanisms, surgical techniques, nano-pharmacological drug delivery systems, and the therapy of diseases like cholesterol using nanotechnology.
Comparisons of Numerical and Solitary Wave Solutions for the Stochastic Reaction-Diffusion Biofilm Model including Quorum Sensing
(Mdpi, 2024) Baber, Muhammad Zafarullah; Ahmed, Nauman; Yasin, Muhammad Waqas; Iqbal, Muhammad Sajid; Akguel, Ali; Cordero, Alicia; Torregrosa, Juan R.
This study deals with a stochastic reaction-diffusion biofilm model under quorum sensing. Quorum sensing is a process of communication between cells that permits bacterial communication about cell density and alterations in gene expression. This model produces two results: the bacterial concentration, which over time demonstrates the development and decomposition of the biofilm, and the biofilm bacteria collaboration, which demonstrates the potency of resistance and defense against environmental stimuli. In this study, we investigate numerical solutions and exact solitary wave solutions with the presence of randomness. The finite difference scheme is proposed for the sake of numerical solutions while the generalized Riccati equation mapping method is applied to construct exact solitary wave solutions. The numerical scheme is analyzed by checking consistency and stability. The consistency of the scheme is gained under the mean square sense while the stability condition is gained by the help of the Von Neumann criteria. Exact stochastic solitary wave solutions are constructed in the form of hyperbolic, trigonometric, and rational forms. Some solutions are plots in 3D and 2D form to show dark, bright and solitary wave solutions and the effects of noise as well. Mainly, the numerical results are compared with the exact solitary wave solutions with the help of unique physical problems. The comparison plots are dispatched in three dimensions and line representations as well as by selecting different values of parameters.
Computational Analysis of the Morphological Aspects of Triadic Hybridized Magnetic Nanoparticles Suspended in Liquid Streamed in Coaxially Swirled Disks
(Mdpi, 2022) Qureshi, Zubair Akbar; Bilal, Sardar; Shah, Imtiaz Ali; Akguel, Ali; Jarrar, Rabab; Shanak, Hussein; Asad, Jihad
Currently, pagination clearly explains the increase in the thermophysical attributes of viscous hybrid nanofluid flow by varying morphological aspects of inducted triadic magnetic nanoparticles between two coaxially rotating disks. Copper metallic nanoparticles are inserted with three different types of metallic oxide nanoparticles: Al2O3, Ti2O, and Fe3O4. Single-phase simulation has been designed for the triadic hybrid nanofluids flow. The achieved expressions are transmuted by the obliging transformation technique because of dimensionless ordinary differential equations (ODEs). Runge-Kutta in collaboration with shooting procedure are implemented to achieve the solution of ODEs. The consequences of pertinent variables on associated distributions and related quantities of physical interest are elaborated in detail. It is inferred from the analysis that Cu-Al2O3 metallic type hybrid nanofluids flow shows significant results as compared with the other hybrid nanoparticles. The injection phenomenon on hybrid nanofluids gives remarkable results regarding shear stress and heat flux with the induction of hybridized metallic nanoparticles. Shape and size factors have also been applied to physical quantities. The morphology of any hybrid nanoparticles is directly proportional to the thermal conductance of nanofluids. Peclet number has a significant effect on the temperature profile.
Computational aspects of an epidemic model involving stochastic partial differential equations
(World Scientific Publ Co Pte Ltd, 2023) Ahmed, Nauman; Yasin, Muhammad W.; Ali, Syed Mansoor; Akguel, Ali; Raza, Ali; Rafiq, Muhammad; Shar, Muhammad Ali
This paper deals with the study of the reaction-diffusion epidemic model perturbed with time noise. It has various applications such as disease in population models of humans, wildlife, and many others. The stochastic SIR model is numerically investigated with the proposed stochastic backward Euler scheme and proposed stochastic implicit finite difference (IFD) scheme. The stability of the proposed methods is shown with Von Neumann criteria and both schemes are unconditionally stable. Both schemes are consistent with systems of the equations in the mean square sense. The numerical solution obtained by the proposed stochastic backward Euler scheme and solutions converges towards an equilibrium but it has negative and divergent behavior for some values. The numerical solution gained by the proposed IFD scheme preserves the positivity and also solutions converge towards endemic and disease-free equilibrium. We have used two problems to check our findings. The graphical behavior of the stochastic SIR model is much adjacent to the classical SIR epidemic model when noise strength approaches zero. The three-dimensional plots of the susceptible and infected individuals are drawn for two cases of endemic equilibrium and disease-free equilibriums. The results show the efficacy of the proposed stochastic IFD scheme.

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