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Öğe Scrutinization of local thermal non-equilibrium effects on stagnation point flow of hybrid nanofluid containing gyrotactic microorganisms: a bio-fuel cells and bio-microsystem technology application(Springer, 2024) Okasha, Mostafa Mohamed; Abbas, Munawar; Formanova, Shoira; Faiz, Zeshan; Ali, Ali Hasan; Akgül, Ali; Galal, Ahmed M.The impact of Stefan blowing on the stagnation point flow of HNF (hybrid nanofluid) across a sheet containing gyrotactic microorganisms under local thermal non-equilibrium conditions (LTNECs) is briefly discussed in this paper. The present work uses a simplified mathematical model to inspect the characteristics of heat transfer in the absence of LTNECs (local thermal equilibrium conditions). LTNECs, traditionally provide two distinct fundamental temperature gradients for the liquid and solid phases simultaneously. A hybrid nanofluid is a mixture of water as the base fluid and single-walled carbon nanotubes and multi-walled carbon nanotubes. Gyrotactic microorganisms are included into nanoparticles to increase their thermal efficiency in a variety of systems, including microbial fuel cells, enzyme biosensors, bacteria powered micromixers, chip-shaped microdevices like bio-microsystems, and micro-volumes like microfluidic devices. This model can also help environmental engineering by enhancing wastewater treatment procedures by allowing microorganisms to break down pollutants more effectively. It advances the development of more productive photo bioreactors, increasing the output of biofuels in the field of renewable energy. Material scientists can utilize this concept to develop controlled nanostructured materials with consistent composition and thermal properties. The considerable similarity transformation is used to build ordinary differential equations for the nonlinear dimensionless system. This problem is solved numerically by using the Bvp4c method. The results determine that when the Stefan blowing parameter increases, fluid flow increases but temperature, mass transfer rate, and heat transfer are decreased.Öğe Deterministic-Stochastic modeling: A new direction in modeling real world problems with crossover effect(Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Araz, Seda IgretMany real world problems depict processes following crossover behaviours. Modelling processes following crossover behaviors have been a great challenge to mankind. Indeed real world problems following crossover from Markovian to randomness processes have been observed in many scenarios, for example in epidemiology with spread of infectious diseases and even some chaos. Deterministic and stochastic methods have been developed independently to develop the future state of the system and randomness respectively. Very recently, Atangana and Seda introduced a new concept called piecewise differentiation and integration, this approach helps to capture processes with crossover effects. In this paper, an example of piecewise modelling is presented with illustration to chaos problems. Some important analysis including a piecewise existence and uniqueness and piecewise numerical scheme are presented. Numerical simulations are performed for different cases.Öğe The effect of Some Boron Derivatives on Kanamycin Resistance and Survival of E. coli and P. aeruginosa in Lake Water(Chinese Center Disease Control & Prevention, 2012) Darcan, Cihan; Kahyaoglu, MustafaObjective To study MIC value of 7 boron derivatives namely [Boric acid (H3BO3), Anhydrous Borax (Na2B4O7), Sodium Borate (NaBO2), Diammonium Tetraborate (NH4)(2)B4O7, Sodium Perborate (NaBO3), Boron Trioxide (B2O3), Potassium Tetraborate (K2B4O7)] on E. coli and P. aeruginosa and their effects on survival of bacteria in lake water and resistance against kanamycin antibiotic. Methods MIC values of Boron derivatives and antibiotic were studied by broth microdilution method. The effect of boron derivatives on survival of bacteria in lake water were also determined with plate count. Results Sodium perborate was determined as the most effective substance among the studied substances. Effectiveness increased as temperature increased. E. coli was more affected from P. aeruginosa in 8 mg/mL sodium perborate concentration in lake water. Moreover, it was determined that MIC value of kanamycin antibiotic decreased 200 times by especially treating P. aeruginosa with sodium perborate in lake water. However, it can be stated that this change in resistance did not arise from microorganisms. Conclusion Sodium perborate solution can be used supportedly in kanamycin antibiotic applications for P. aeruginosa. Future studies are necessary to explore the relation between sodium perborate and kanamycin which is effective on P. aeruginosa in lake water.Öğe Piecewise derivatives versus short memory concept: analysis and application(Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Araz, Seda İğretWe have provided a detailed analysis to show the fundamental difference between the concept of short memory and piecewise differential and integral operators. While the concept of short memory leads to different long tails in different intervals of time or space as a result of a power law with different fractional orders, the concept of piecewise helps to depict crossover behaviors of different patterns. We presented some examples with different numerical simulations. In some cases piecewise models led to transitional behavior from deterministic to stochastic, this is indeed the reason why this concept was introduced.Öğe Approximation of fixed point of generalized non-expansive mapping via new faster iterative scheme in metric domain(Amer Inst Mathematical Sciences-Aims, 2023) Muhammad, Noor; Asghar, Ali; Irum, Samina; Akgul, Ali; Khalil, E. M.; Inc, MustafaIn this paper, we establish a new iterative process for approximation of fixed points for contraction mappings in closed, convex metric space. We conclude that our iterative method is more accurate and has very fast results from previous remarkable iteration methods like Picard-S, Thakur new, Vatan Two-step and K-iterative process for contraction. Stability of our iteration method and data dependent results for contraction mappings are exact, correspondingly on testing our iterative method is advanced. Finally, we prove enquiring results for some weak and strong convergence theorems of a sequence which is generated from a new iterative method, Suzuki generalized non-expansive mappings with condition (C) in uniform convexity of metric space. Our results are addition, enlargement over and above generalization for some well-known conclusions with literature for theory of fixed point.Öğe Rhythmic behaviors of the human heart with piecewise derivative(Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Igret Araz, SedaIt has been noticed that heartbeats can display different patterns according to situations faced by a human. It has been indicated that, those passages from one pattern to another cannot be modelled using a single differential operator, either classical, fractional, or stochastic. In 2021, alternative concepts were introduced and called piecewise differentiation and integration, these concepts were applied in several complex problems with great insight. It is strongly believed that such will be leading concepts to modelling real-world problems with crossover behaviors. Crossover behaviors have been observed in heart rhythm, therefore, in this paper, the well-known van Der Pol equation will be subjected to piecewise analysis. Several simulations will be obtained using a numerical scheme based on Newton polynomial interpolation. Obtained figures show real world behaviors of heart rhythm with piecewise patterns.Öğe On the Caputo-Hadamard fractional IVP with variable order using the upper-lower solutions technique(Amer Inst Mathematical Sciences-Aims, 2023) Bouazza, Zoubida; Souhila, Sabit; Etemad, Sina; Souid, Mohammed Said; Akguel, Ali; Rezapour, Shahram; De la Sen, ManuelThis paper studies the existence of solutions for Caputo-Hadamard fractional nonlinear differential equations of variable order (CHFDEVO). We obtain some needed conditions for this purpose by providing an auxiliary constant order system of the given CHFDEVO. In other words, with the help of piece-wise constant order functions on some continuous subintervals of a partition, we convert the main variable order initial value problem (IVP) to a constant order IVP of the Caputo-Hadamard differential equations. By calculating and obtaining equivalent solutions in the form of a Hadamard integral equation, our results are established with the help of the upper-lower-solutions method. Finally, a numerical example is presented to express the validity of our results.Öğe A novel numerical method for solving the Caputo-Fabrizio fractional differential equation(Amer Inst Mathematical Sciences-Aims, 2023) Arshad, Sadia; Saleem, Iram; Akgul, Ali; Huang, Jianfei; Tang, Yifa; Eldin, Sayed M.In this paper, a unique and novel numerical approach-the fractional-order Caputo-Fabrizio derivative in the Caputo sense-is developed for the solution of fractional differential equations with a non-singular kernel. After converting the differential equation into its corresponding fractional integral equation, we used Simpson's 1/3 rule to estimate the fractional integral equation. A thorough study is then conducted to determine the convergence and stability of the suggested method. We undertake numerical experiments to corroborate our theoretical findings.Öğe 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.Öğe A successive midpoint method for nonlinear differential equations with classical and Caputo-Fabrizio derivatives(Amer Inst Mathematical Sciences-Aims, 2023) Atangana, Abdon; Araz, Seda IgretIn this study, we present a numerical scheme for solving nonlinear ordinary differential equations with classical and Caputo-Fabrizio derivatives using consecutive interval division and the midpoint approach. By doing so, we increased the accuracy of the midpoint approach, which is dependent on the number of interval divisions. In the example of the Caputo-Fabrizio differential operator, we established the existence and uniqueness of the solution using the Caratheodory-Tonelli sequence. We solved numerous nonlinear equations and determined the global error to test the accuracy of the proposed scheme. When the differential equation met the circumstances under which it was generated, the results revealed that the procedure was quite accurate.Öğe Piecewise differential equations: theory, methods and applications(Amer Inst Mathematical Sciences-Aims, 2023) Atangana, Abdon; Araz, Seda IgretAcross many real-world problems, crossover tendencies are seen. Piecewise differential operators are constructed by using different kernels that exhibit behaviors arising in several real -world problems; thus, crossover behaviors could be well modeled using these differential and integral operators. Power-law processes, fading memory processes and processes that mimic the generalized Mittag-Leffler function are a few examples. However, the use of piecewise differential and integral operators cannot be applied to all processes involving crossovers. For instance, a considerable alteration eventually manifests when groundwater over-abstraction causes it to flow from confined to unconfined aquifers. The idea of piecewise differential equations, which can be thought of as an extension of piecewise functions to the framework of differential equations, is introduced in this work. While we concentrate on ordinary differential equations, it is important to note that partial differential equations can also be constructed with the same technique. For both integer and non-integer instances, piecewise differential equations have been introduced. We have explained the usage of the Laplace transform for the linear case and demonstrated how a new class of Bode diagrams could be produced. We have provided some examples of numerical solutions as well as conditions for the existence and uniqueness of their solutions. We discussed a few scenarios in which we used chaos and non-linear ordinary differential equations to produce novel varieties of chaos. We believe that this idea could lead to some significant conclusions in the future.Öğe Advanced analysis in epidemiological modeling: detection of waves(Amer Inst Mathematical Sciences-Aims, 2022) Atangana, Abdon; Araz, Seda IgretMathematical concepts have been used in the last decades to predict the behavior of the spread of infectious diseases. Among them, the reproductive number concept has been used in several published papers to study the stability of the mathematical model used to predict the spread patterns. Some conditions were suggested to conclude if there would be either stability or instability. An analysis was also meant to determine conditions under which infectious classes will increase or die out. Some authors pointed out limitations of the reproductive number, as they presented its inability to help predict the spread patterns. The concept of strength number and analysis of second derivatives of the mathematical models were suggested as additional tools to help detect waves. This paper aims to apply these additional analyses in a simple model to predict the future.Öğe Analytical study of a Hepatitis B epidemic model using a discrete generalized nonsingular kernel(Amer Inst Mathematical Sciences-Aims, 2024) Farman, Muhammad; Akgul, Ali; Conejero, J. Alberto; Shehzad, Aamir; Nisar, Kottakkaran Sooppy; Baleanu, DumitruHepatitis B is a worldwide viral infection that causes cirrhosis, hepatocellular cancer, the need for liver transplantation, and death. This work proposed a mathematical representation of Hepatitis B Virus (HBV) transmission traits emphasizing the significance of applied mathematics in comprehending how the disease spreads. The work used an updated Atangana-Baleanu fractional difference operator to create a fractional -order model of HBV. The qualitative assessment and wellposedness of the mathematical framework were looked at, and the global stability of equilibrium states as measured by the Volterra -type Lyapunov function was summarized. The exact answer was guaranteed to be unique using the Lipschitz condition. Additionally, there were various analyses of this new type of operator to support the operator's efficacy. We observe that the explored discrete fractional operators will be x 2 -increasing or decreasing in certain domains of the time scale N j : = j , j + 1 ,... by looking at the fundamental characteristics of the proposed discrete fractional operators along with x -monotonicity descriptions. For numerical simulations, solutions were constructed in the discrete generalized form of the Mittag-Leffler kernel, highlighting the impacts of the illness caused by numerous causes. The order of the fractional derivative had a significant influence on the dynamical process utilized to construct the HBV model. Researchers and policymakers can benefit from the suggested model's ability to forecast infectious diseases such as HBV and take preventive action.Öğe A cotangent fractional Gronwall inequality with applications(Amer Inst Mathematical Sciences-Aims, 2024) Sadek, Lakhlifa; Akgul, Ali; Bataineh, Ahmad Sami; Hashim, IshakThis article presents the cotangent fractional Gronwall inequality, a novel understanding of the Gronwall inequality within the context of the cotangent fractional derivative. We furnish an explanation of the cotangent fractional derivative and emphasize a selection of its distinct characteristics before delving into the primary findings. We present the cotangent fractional Gronwall inequality (Lemma 3.1) and a Corollary 3.2 using the Mittag-Leffler function, we establish singularity and compute an upper limit employing the Mittag-Leffler function for solutions in a nonlinear delayed cotangent fractional system, illustrating its practical utility. To underscore the real -world relevance of the theory, a tangible instance is given.Öğe Numerical study of a nonlinear fractional chaotic Chua's circuit(Amer Inst Mathematical Sciences-Aims, 2023) Shah, Nehad Ali; Ahmed, Iftikhar; Asogwa, Kanayo K.; Zafar, Azhar Ali; Weera, Wajaree; Akgul, AliAs an exponentially growing sensitivity to modest perturbations, chaos is pervasive in nature. Chaos is expected to provide a variety of functional purposes in both technological and biological systems. This work applies the time-fractional Caputo and Caputo-Fabrizio fractional derivatives to the Chua type nonlinear chaotic systems. A numerical analysis of the mathematical models is used to compare the chaotic behavior of systems with differential operators of integer order versus systems with fractional differential operators. Even though the chaotic behavior of the classical Chua's circuit has been extensively investigated, our generalization can highlight new aspects of system behavior and the effects of memory on the evolution of the chaotic generalized circuit.Öğe Extension of Chaplygin's existence and uniqueness method for fractal-fractional nonlinear differential equations(Amer Inst Mathematical Sciences-Aims, 2024) Atangana, Abdon; Araz, Seda IgretThe existence and uniqueness of solutions to nonlinear ordinary differential equations with fractal-fractional derivatives, with Dirac-delta, exponential decay, power law, and generalized Mittag-Leffler kernels, have been the focus of this work. To do this, we used the Chaplygin approach, which entails creating two lower and upper sequences that converge to the solution of the equations under consideration. We have for each case provided the conditions under which these sequences are obtained and converge.Öğe A finite difference scheme to solve a fractional order epidemic model of computer virus(Amer Inst Mathematical Sciences-Aims, 2023) Iqbal, Zafar; Rehman, Muhammad Aziz-ur; Imran, Muhammad; Ahmed, Nauman; Fatima, Umbreen; Akgul, Ali; Rafiq, MuhammadIn this article, an analytical and numerical analysis of a computer virus epidemic model is presented. To more thoroughly examine the dynamics of the virus, the classical model is transformed into a fractional order model. The Caputo differential operator is applied to achieve this. The Jacobian approach is employed to investigate the model's stability. To investigate the model's numerical solution, a hybridized numerical scheme called the Grunwald Letnikov nonstandard finite difference (GL-NSFD) scheme is created. Some essential characteristics of the population model are scrutinized, including positivity boundedness and scheme stability. The aforementioned features are validated using test cases and computer simulations. The mathematical graphs are all detailed. It is also investigated how the fundamental reproduction number R0 functions in stability analysis and illness dynamics.Öğe Efficient spectral collocation method for nonlinear systems of fractional pantograph delay differential equations(Amer Inst Mathematical Sciences-Aims, 2024) Zaky, M. A.; Babatin, M.; Hammad, M.; Akgul, A.; Hendy, A. S.Caputo-Hadamard-type fractional calculus involves the logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenges in numerical approximations. In this paper, we construct and analyze a spectral collocation approach using mapped Jacobi functions as basis functions and construct an efficient algorithm to solve systems of fractional pantograph delay differential equations involving Caputo-Hadamard fractional derivatives. What we study is the error estimates of the derived method. In addition, we tabulate numerical results to support our theoretical analysis.Öğe Analysis of HIV/AIDS model with Mittag-Leffler kernel(Amer Inst Mathematical Sciences-Aims, 2022) Akram, Muhammad Mannan; Farman, Muhammad; Akgul, Ali; Saleem, Muhammad Umer; Ahmad, Aqeel; Partohaghigh, Mohammad; Jarad, FahdRecently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.Öğe Solving the time-fractional inverse Burger equation involving fractional Heydari-Hosseininia derivative(Amer Inst Mathematical Sciences-Aims, 2022) Partohaghighi, Mohammad; Akgul, Ali; Asad, Jihad; Wannan, RaniaHeydari-Hosseininia (HH) fractional derivative is a newly introduced concept of fractional calculus which conquers the restrictions of non-singular fractional derivatives in the Caputo-Fabrizio (CF) and Atangana-Baleanu senses. For instance, it is not easy to get the closed-form of the fractional derivative of functions using CF because of the construction of its kernel function. In this paper, we present a powerful numerical scheme based on energy boundary functions to get the approximate solutions of the time-fractional inverse Burger equation containing HH-derivative: (HH)D(tau)(alpha)h(z, tau) - h(z, tau)h(z)(z, tau) = h(zz)(z, tau) + H(z, tau), which (HH)D(alpha)(tau )is the HH-derivative with regard to alpha-order. This problem has never been investigated earlier so, this is our motivation to work on this important problem. Some numerical examples are presented to verify the efficiency of the presented technique. Graphs of the exact and numerical solutions along with the plot of absolute error are provided for each example. Tables are given to see and compare the results point by point for each example.
