Yazar "Hassani, Murad Khan" seçeneğine göre listele
Listeleniyor 1 - 20 / 25
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe A comprehensive study of subdivision collocation method for Burgers' equation(Taylor & Francis Inc, 2024) Ejaz, Syeda Tehmina; Bibi, Saima; Akgul, Ali; Hassani, Murad KhanThis study explores the use of subdivision schemes to efficiently solve Burgers' equation. Burgers' equation is a fundamental fluid dynamics equation that describes the nonlinear behavior of fluid flow. This type of nonlinear equation is difficult to solve analytically, which makes the numerical solution an important tool. The subdivision collocation method (SCM) converts Burgers' equation into a system of algebraic linear equations using the quasilinearization technique. The results of this study demonstrate that the proposed approach yields accurate numerical solutions for Burgers' equation. Additionally, the subdivision approach is computationally efficient and requires fewer computational resources than existing numerical methods, making it a promising tool for solving Burgers' equation in practical applications. Overall, this study provides valuable insights into the approximate solution of Burgers' equation by implementing subdivision schemes.Öğe A plethora of novel solitary wave solutions related to van der Waals equation: a comparative study(Nature Portfolio, 2024) Butt, Asma Rashid; Jhangeer, Adil; Akgul, Ali; Hassani, Murad KhanIn this article, we explore exact solitary wave solutions to the van der Waals equation which is crucial for numerous applications involving a variety of physical occurrences. This system is used to define the behavior of real gases taking into consideration finite size of molecules and also has some applications in industry for granular materials. The model is studied under the effect of fractional derivatives by employing two different definitions: beta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta$$\end{document}, and M-truncated. Further, new extended direct algebraic method is employed to construct the solitary wave solutions for the model. The solutions transmit several novel solutions, such as dark-singular, dark-bright, singular-periodic and dark solutions, and this method establishes the conditions required for the formation of these structures. To show the comparative analysis between two different fractional operators, results are graphically represented in the form of 2-dimensional and 3-dimensional visualizations.Öğe A review on analysis and modeling of electrical machine insulation system(Taylor & Francis Ltd, 2024) Raziq, Hira; Batool, Munira; Nawaz, Fawad; Akgul, Ali; Afzal, Farkhanda; Hassani, Murad KhanElectrical machines are usually operated in a very harsh environment, therefore great attention has to be given towards the designing of insulating materials and insulation systems. The severe operating environment invites corrosion, humidity, high temperature, and so on. This article is a review of electrical machine's insulation design, techniques, and methodologies for modeling and testing the insulation materials and the recent advancements in this field. Several testing standards and methods to detect insulation failure have been discussed. Case studies of insulation failure in the electrical machine have been discussed to draw the reader's attention towards a more realistic approach. Issues related to high voltage insulation systems used in industries like aerospace electric powertrain, hydro generators and, wind turbine generators have been briefed in the article. Partial discharge monitoring techniques are explored in this article. Its consequences on most emerging and advanced high voltage, high-altitude aerospace applications, will be discussed. Finally, polymer nanocomposite materials with exceptional dielectric strength or thermal conductivity are underlined as an outlook for future consideration in machine insulation design.Öğe Abundant soliton solution for the time-fractional stochastic Gray-Scot model under the influence of noise and M-truncated derivative(Springer, 2024) Baber, Muhammad Zafarullah; Ahmed, Nauman; Yasin, Muhammad Waqas; Ali, Syed Mansoor; Ali, Mubasher; Akgul, Ali; Hassani, Murad KhanIn this study, we investigate the abundant soliton solutions for the time-fractional stochastic Gray-Scot (TFSGS) model analytically. The Gray-Scot model is considered under the influence of M-truncated derivative and multiplicative time noise. This is a reaction-diffusion chemical concentration model that explains the irreversible chemical reaction process. The M-truncated derivative is applied for the fractional version while Brownian motion is taken in the sense of time noise. The novel mathematical technique is used to obtain the abundant families of soliton solutions. These solutions are explored in the form of shock, complicated solitary-shock, shock-singular, and periodic-singular types of single and combination wave structures. During the derivation, the rational solutions also appear. Moreover, we use MATHEMATICA 11.1 tools to plot our solutions and exhibit several three-dimensional, two-dimensional, and their corresponding contour graphs to show the fractional derivative and Brownian motion impact on the soliton solutions of the TFSGS model. We show that the TFDGS model solutions are stabilized at around zero by the multiplicative Brownian motion. These wave solutions represent the chemical concentrations of the reactants. The TFDGS model is considered to find the exact solitsary wave solutions under the random environment.The new MEDA method is used to obtain the different form of solutions.The different graphical behaviour are drawn to show the effects of noise and fractional derivatives.Öğe 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 KhanIn 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.Öğe Analytical investigation of Carreau fluid flow through a non-circular conduit with wavy wall(Nature Portfolio, 2024) Shahzad, Muhammad Hasnain; Awan, Aziz Ullah; Akgul, Ali; Nadeem, Sohail; Guedri, Kamel; Hassani, Murad Khan; Makhdoum, Basim M.Peristaltic flow through an elliptic channel has vital significance in different scientific and engineering applications. The peristaltic flow of Carreau fluid through a duct with an elliptical cross-section is investigated in this work . The proposed problem is defined mathematically in Cartesian coordinates by incorporating no-slip boundary conditions. The mathematical equations are solved in their dimensionless form under the approximation of long wavelength. The solution of the momentum equation is obtained by applying perturbation technique (We2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W_e<^>2$$\end{document} as perturbation parameter) along with a polynomial solution. We introduce a new polynomial of twenty degrees to solve the energy equation. The solutions of mathematical equations are investigated deeply through graphical analysis. It is noted that non-Newtonian effects are dominant along the minor axis. It is found that flow velocity is higher in the channels having a high elliptical cross-section. It is observed from the streamlines that the flow is smooth in the mid-region, but they transform into contours towards the peristaltic moving wall of the elliptic duct.Öğe Cholera disease dynamics with vaccination control using delay differential equation(Nature Portfolio, 2024) Singh, Jaskirat Pal; Kumar, Sachin; Akgul, Ali; Hassani, Murad KhanThe COVID-19 pandemic came with many setbacks, be it to a country's economy or the global missions of organizations like WHO, UNICEF or GTFCC. One of the setbacks is the rise in cholera cases in developing countries due to the lack of cholera vaccination. This model suggested a solution by introducing another public intervention, such as adding Chlorine to water bodies and vaccination. A novel delay differential model of fractional order was recommended, with two different delays, one representing the latent period of the disease and the other being the delay in adding a disinfectant to the aquatic environment. This model also takes into account the population that will receive a vaccination. This study utilized sensitivity analysis of reproduction number to analytically prove the effectiveness of control measures in preventing the spread of the disease. This analysis provided the mathematical evidence for adding disinfectants in water bodies and inoculating susceptible individuals. The stability of the equilibrium points has been discussed. The existence of stability switching curves is determined. Numerical simulation showed the effect of delay, resulting in fluctuations in some compartments. It also depicted the impact of the order of derivative on the oscillations.Öğe 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 KhanA 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.Öğe Computational analysis of corruption dynamics insight into fractional structures(Taylor & Francis Ltd, 2024) Akgul, Ali; Farman, Muhammad; Sutan, Muhammad; Ahmad, Aqeel; Ahmad, Sheraz; Munir, Arshad; Hassani, Murad KhanThe fractional derivative that is used to compute the solution of the corruption system with Power-Law Kernel, Mittag-Leffler Kernel, and Exponential Decay Kernel. It is important to study and analyse corruption dynamics, because it is an act that has a direct effect on public rights, and because of this the right of the rightful owner, just got destroyed. Using hypothesis theory for differential equation, this work suggests and assesses a nonlinear deterministic model for the dynamics of corruption. Positivity and boundedness are verified for the proposed corruption model to identify the level of resolution of corruption factor in society. Fractional-order corruption model is investigated with different kernels for efficient results. The necessary criteria for the best control of corruption transmission were identified using Pontryagin's maximal concept. The numerical simulation showed that corruption must be resisted by an integrated control strategy. Numerical simulations are used to demonstrate the correctness of the proposed approaches. Finally, simulations are derived for the proposed schemes to check the effectiveness of the results and to analyse the corruption behaviour in society as well as dynamically highlight the propagation of corruption group.Öğe Correction to: Analysis of some dynamical systems by combination of two different methods (Scientific Reports, (2024), 14, 1, (18710), 10.1038/s41598-024-62042-x)(Nature Research, 2024) Ganie, Abdul Hamid; Zidan, A.M.; Shah, Rasool; Akgül, Ali; Hassani, Murad KhanCorrection to: Scientific Reportshttps://doi.org/10.1038/s41598-024-62042-x, published online 12 August 2024 In the original version of this Article A. M. Zidan was incorrectly affiliated with ‘Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon’. The correct affiliation is listed below. Department of Mathematics, College of Science, King Khalid University, P.O. Box: 9004, 61413 Abha, Saudi Arabia. In addition, the Acknowledgements section contained an error. “The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under Grant No. RGP.2/13/44.” now reads: “The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through large group Research Project under grant number RGP.2/16/45.” The original Article has been corrected. © The Author(s) 2024.Öğe Dual solution of thin film flow of fuzzified MHD pseudo-plastic fluid: numerical investigation in uncertain environment(Taylor & Francis Ltd, 2024) Qayyum, Mubashir; Tahir, Aneeza; Saeed, Syed Tauseef; Afzal, Sidra; Akgul, Ali; Hassani, Murad KhanThe pseudoplastic fluids have wide range of applications in industrial areas including cyclone separation, bearings, paper fibre separation, heat exchangers and also in food industry. In this regard, the current manuscript investigates the impact of transverse magnetic field on thin pseudo-plastic film flow on a vertical wall in a fuzzy (uncertain) environment. The uncertainty in a model is characterized through triangular fuzzy numbers (TFNs) along with $ \mathbbm {r} $ r-cut approach, which is computationally effective in capturing the uncertainties in physical phenomena. This results in the modelling of highly nonlinear fuzzified problem. For solution and analysis purposes, Runge-Kutta Fehlberg (RKF) is utilized. Also, RKF solutions are validated by comparing them to homotopy perturbation solutions in the current manuscript. The impact of $ \mathbbm {r} $ r-cut, and fluid parameters including non-Newtonian parameter beta, magnetic field M and Stoke's number $ \mathcal {S}_{t} $ St on the upper and lower velocity profiles are captured and analysed numerically and graphically. Analysis reveals that velocity profile decreases with an increase in applied magnetic field at upper and lower bounds. Also, increase in $ \mathcal {S}_{t} $ St and beta increases the velocity profile at lower bound, while inverse behaviour is recorded in the case of upper bound. The results also indicate that as $ \mathbbm {r} $ r goes from 0 to 1, the crisp solution always lies between upper and lower profiles, and becomes coherent at 1. Moreover, all fuzzy level set values of $ \mathbbm {r} \in [0,1] $ r is an element of[0,1] satisfy the fuzzy solution in the form of TFN.Öğe Exploring the advection-diffusion equation through the subdivision collocation method: a numerical study(Nature Portfolio, 2024) Malik, Safia; Ejaz, Syeda Tehmina; Akgul, Ali; Hassani, Murad KhanThe current research presents a novel technique for numerically solving the one-dimensional advection-diffusion equation. This approach utilizes subdivision scheme based collocation method to interpolate the space dimension along with the finite difference method for the time derivative. The proposed technique is examined on a variety of problems and the obtained results are presented both quantitatively in tables and visually in figures. Additionally, a comparative analysis is conducted between the numerical outcomes of the proposed technique with previously published methods to validate the correctness and accuracy of the current approach. The primary objective of this research is to investigate the application of subdivision schemes in the fields of physical sciences and engineering. Our approach involves transforming the problem into a set of algebraic equations.Öğe Flip bifurcation analysis and mathematical modeling of cholera disease by taking control measures(Nature Portfolio, 2024) Ahmad, Aqeel; Abbas, Fakher; Farman, Muhammad; Hincal, Evren; Ghaffar, Abdul; Akgul, Ali; Hassani, Murad KhanTo study the dynamical system, it is necessary to formulate the mathematical model to understand the dynamics of various diseases which are spread in the world wide. The objective of the research study is to assess the early diagnosis and treatment of cholera virus by implementing remedial methods with and without the use of drugs. A mathematical model is built with the hypothesis of strengthening the immune system, and a ABC operator is employed to turn the model into a fractional-order model. A newly developed system SEIBR, which is examined both qualitatively and quantitatively to determine its stable position as well as the verification of flip bifurcation has been made for developed system. The local stability of this model has been explored concerning limited observations, a fundamental aspect of epidemic models. We have derived the reproductive number using next generation method, denoted as R 0 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_{0}$$\end{document} , to analyze its impact rate across various sub-compartments, which serves as a critical determinant of its community-wide transmission rate. The sensitivity analysis has been verified according to its each parameters to identify that how much rate of change of parameters are sensitive. Atangana-Toufik scheme is employed to find the solution for the developed system using different fractional values which is advanced tool for reliable bounded solution. Also the error analysis has been made for developed scheme. Simulations have been made to see the real behavior and effects of cholera disease with early detection and treatment by implementing remedial methods without the use of drugs in the community. Also identify the real situation the spread of cholera disease after implementing remedial methods with and without the use of drugs. Such type of investigation will be useful to investigate the spread of virus as well as helpful in developing control strategies from our justified outcomes.Öğe Generation of fractal curves using new binary 8-point interpolatory subdivision scheme(Taylor & Francis Ltd, 2024) Ghaffar, Abdul; Javed, Sadia; Mustafa, Ghulam; Akgul, Ali; Hassani, Murad KhanThe subdivision scheme is a valuable tool for designing shapes and representing geometry in computer-aided geometric design. It has excellent geometric properties, such as fractals and adjustable shape. In this research paper, we explore the generation of fractal curves using a novel binary 8-point interpolatory subdivision scheme with two parameters. We analyse different properties of the proposed scheme, including convergence, special cases, and fractals. Additionally, we demonstrate through various examples the relationship between the shape parameters and the fractal behaviour of the resulting curve. Our research also identifies a specific range of shape parameters that can effectively produce fractal curves. The findings of this study provide a fast and efficient method for generating fractals, as demonstrated by numerous examples. Modelling examples show that the 8-point interpolatory scheme can enhance the efficiency of computer design for complex models.Öğe Investigating double-diffusive natural convection in a sloped dual-layered homogenous porous-fluid square cavity(Nature Portfolio, 2024) Jalili, Bahram; Emad, Majdeddin; Malekshah, Emad Hasani; Jalili, Payam; Akgul, Ali; Hassani, Murad KhanThis article investigates natural convection with double-diffusive properties numerically in a vertical bi-layered square enclosure. The cavity has two parts: one part is an isotropic and homogeneous porous along the wall, and an adjacent part is an aqueous fluid. Adiabatic, impermeable horizontal walls and constant and uniform temperatures and concentrations on other walls are maintained. To solve the governing equations, the finite element method (FEM) employed and predicted results shows the impact of typical elements of convection on double diffusion, namely the porosity thickness, cavity rotation angle, and thermal conductivity ratio. Different Darcy and Rayleigh numbers effects on heat transfer conditions were investigated, and the Nusselt number in the border of two layers was obtained. The expected results, presented as temperature field (isothermal lines) and velocity behavior in X and Y directions, show the different effects of the aforementioned parameters on double diffusion convective heat transfer. Also results show that with the increase in the thickness of the porous layer, the Nusselt number decreases, but at a thickness higher than 0.8, we will see an increase in the Nusselt number. Increasing the thermal conductivity ratio in values less than one leads to a decrease in the average Nusselt number, and by increasing that parameter from 1 to 10, the Nusselt values increase. A higher rotational angle of the cavity reduces the thermosolutal convective heat transfer, and increasing the Rayleigh and Darcy numbers, increases Nusselt. These results confirm that the findings obtained from the Finite Element Method (FEM), which is the main idea of this research, are in good agreement with previous studies that have been done with other numerical methods.Öğe Mathematical modelling and control approach for sustainable ecosystems in mitigating the impact of pollutants on aquatic species in rivers(Nature Portfolio, 2024) Karim, Marouane; Dehaj, Imane; Akguel, Ali; Hassani, Murad Khan; Ferjouchia, Hanane; Rachik, MostafaThis paper focuses on the urgent issue of minimising the impact of pollutants on aquatic life in river ecosystems. Our innovative approach involves the integration of mathematical modelling and strategic control methods to counteract the negative consequences of industrial and agricultural activities. The model, developed in a one-dimensional context, captures the complex dynamics of species population and pollutant concentration. Using an optimisation framework, we strive to achieve a harmonious balance that limits pollution, enhances species diversity and optimises control expenditure. Ultimately, we seek to harmonise industrial progress with ecological vitality, promoting the sustainability of river ecosystems for generations to come.Öğe Multi-alpha fractal iteration algorithm(Taylor & Francis Ltd, 2024) Shahzeen, Sundus; Muslim, Humaira; Ali, Asad; Akguel, Ali; Hassani, Murad KhanIn numerous domains, such as an image compression or encryption, art, research, and many more, complex visualizations of nonlinear dynamical systems play an important role. Antifractals have recently become a popular topic of study. We generate them by applying an iteration to an initial point in the complex plane. The main aim is to explore the dynamics of antifractals such as Julia sets, tricorns, and multicorns of polynomials using a multi-alpha fractal iteration algorithm (python code). In this study we develop an Ali-algorithm that can be used not only to generate more antifractals by using different values but generate new antifractals by changing the values in the iteration. The scheme used is the CR iteration with s-convexity. The escape criterion is vital in generating antifractals, which are at the center of various image encryption and computer graphics applications. We determine a generic form of such criterion in CR orbit. Many stunning aesthetic patterns are generated for antipolynomials of complex plane $\bar{\varphi}<^>2+\bar{\varphi}+c$phi2+phi+c to investigate the geometry of antifractalsand and their respective standard deviations are also mentioned.Öğe Neuro-computing solution for Lorenz differential equations through artificial neural networks integrated with PSO-NNA hybrid meta-heuristic algorithms: a comparative study(Nature Portfolio, 2024) Aslam, Muhammad Naeem; Aslam, Muhammad Waheed; Arshad, Muhammad Sarmad; Afzal, Zeeshan; Hassani, Murad Khan; Zidan, Ahmed M.; Akgul, AliIn this article, examine the performance of a physics informed neural networks (PINN) intelligent approach for predicting the solution of non-linear Lorenz differential equations. The main focus resides in the realm of leveraging unsupervised machine learning for the prediction of the Lorenz differential equation associated particle swarm optimization (PSO) hybridization with the neural networks algorithm (NNA) as ANN-PSO-NNA. In particular embark on a comprehensive comparative analysis employing the Lorenz differential equation for proposed approach as test case. The nonlinear Lorenz differential equations stand as a quintessential chaotic system, widely utilized in scientific investigations and behavior of dynamics system. The validation of physics informed neural network (PINN) methodology expands to via multiple independent runs, allowing evaluating the performance of the proposed ANN-PSO-NNA algorithms. Additionally, explore into a comprehensive statistical analysis inclusive metrics including minimum (min), maximum (max), average, standard deviation (S.D) values, and mean squared error (MSE). This evaluation provides found observation into the adeptness of proposed AN-PSO-NNA hybridization approach across multiple runs, ultimately improving the understanding of its utility and efficiency.Öğe New insights into fractional twin-core couplers: bifurcation and sensitivity analysis(Springer, 2024) Zhou, Zizhao; Abbas, M. S.; El-Rashidy, K.; Qadri, Intakhab Alam; Abuzar, Muhammad; Akguel, Ali; Hassani, Murad KhanThis paper analyses the analytical solutions of the fractional twin-core coupler (fTCC) equations, which include Kerr law nonlinearity, utilising the unified and sub-ODE methods along with beta and M-truncated fractional derivatives. The visually detailed report highlights certain solutions adorned with carefully selected parametric values to demonstrate their distribution. The main concept of this enhancement involves adopting a new formal structure for the preferred solution and considering the dynamic aspects of the problem. To achieve a more profound comprehension of physical implications of these solutions, we have depicted them through diverse visualisations, including 3D and 2D plots. Subsequently, a planar dynamical system is introduced, and bifurcation analysis is performed to determine the bifurcation structures of the nonlinear and super-nonlinear travelling wave solutions of the proposed model. Every potential phase portrait is displayed using specific parameter values. Finally, the model is transformed via the Galilean transformation into a planer dynamical system and the sensitivity performance is assessed.Öğe Novel adaptive control approach to fractal fractional order deforestation model and its impact on soil erosion(Nature Portfolio, 2024) Priya, P.; Sabarmathi, A.; Akgul, Ali; Hassani, Murad KhanDeforestation exerts profound ramifications on soil quality and biodiversity, thereby exerting substantial economic repercussions. The depletion of organic matter and structural integrity of soil following tree removal for agricultural purposes underscores the severity of this issue. In elucidating the soil pollution stemming from deforestation, this research employs a sophisticated five-compartment SDIFR model integrating fractal dimension and fractional order dynamics. The rigorous analysis, including the application of Picard Lindelof's fixed point theorem, establishes the existence and uniqueness of explicit solutions. Furthermore, the examination of local and global stability sheds light on the system's behavior, delineating between pollution-free equilibrium and pollution-extinct equilibrium states. To regulate system behavior, an adaptive control framework grounded in fractal fractional order is proposed, leveraging the Adams-Bashforth numerical approximation scheme for implementation. Through numerical simulations, the study underscores the pivotal role of parameters, thus substantiating the significance of the proposed model in comprehensively addressing the complexities of soil pollution induced by deforestation.
