Browsing by Author "Ahmad, Shabir"

Now showing 1 - 14 of 14

Citation - WoS: 20
Citation - Scopus: 25
A hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations
(Amer inst Mathematical Sciences-aims, 2022) Ahmad, Shabir; Jarad, Fahd; Ullah, Aman; Akgul, Ali; Jarad, Fahd; 234808; Matematik
It is important to deal with the exact solution of nonlinear PDEs of non-integer orders. Integral transforms play a vital role in solving differential equations of integer and fractional orders. 'o obtain analytical solutions to integer and fractional-order DEs, a few transforms, such as Laplace transforms, Sumudu transforms, and Elzaki transforms, have been widely used by researchers. We propose the Yang transform homotopy perturbation (YTHP) technique in this paper. We present the relation of Yang transform (YT) with the Laplace transform. We find a formula for the YT of fractional derivative in Caputo sense. We deduce a procedure for computing the solution of fractional-order nonlinear PDEs involving the power-law kernel. We show the convergence and error estimate of the suggested method. We give some examples to illustrate the novel method. We provide a comparison between the approximate solution and exact solution through tables and graphs.
Citation - WoS: 29
Citation - Scopus: 32
A novel method for analysing the fractal fractional integrator circuit
(Elsevier, 2021) Akgul, Ali; Baleanu, Dumitru; Ahmad, Shabir; Ullah, Aman; Baleanu, Dumitru; Akgul, Esra Karatas; 56389; Matematik
In this article, we propose the integrator circuit model by the fractal-fractional operator in which fractional-order has taken in the Atangana-Baleanu sense. Through Schauder's fixed point theorem, we establish existence theory to ensure that the model posses at least one solution and via Banach fixed theorem, we guarantee that the proposed model has a unique solution. We derive the results for Ulam-Hyres stability by mean of non-linear functional analysis which shows that the proposed model is Ulam-Hyres stable under the new fractal-fractional derivative. We establish the numerical results of the model under consideration through Atanaga-Toufik method. We simulate the numerical results for different sets of fractional order and fractal dimension.(C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 22
Citation - Scopus: 22
A numerical study of dengue internal transmission model with fractional piecewise derivative
(Elsevier, 2022) Ahmad, Shabir; Jarad, Fahd; Yassen, Mansour F.; Alam, Mohammad Mahtab; Alkhati, Soliman; Jarad, Fahd; Riaz, Muhammad Bilal; 234808; Matematik
The goal of this paper is to study the dynamics of the dengue internal transmission model using a novel piecewise derivative approach in the sense of singular and non-singular kernels. The singular kernel operator is in the sense of Caputo, whereas the non-singular kernel operator is the Atangana-Baleanu Caputo operator. The existence and uniqueness of a solution with piecewise derivative is presented for the considered problem by using fixed point theorems. The suggested problem's approximate solution is demonstrated using the piecewise numerical iterative Newton polynomial approach. A numerical scheme for piecewise derivatives is established in terms of singular and non-singular kernels. The numerical simulation for the piecewise derivable problem under consideration is depicted using data for various fractional orders. This work makes the idea of piecewise derivatives and the dynamics of the crossover problem much clearer.
Citation - WoS: 26
Citation - Scopus: 29
Analysis of a conformable generalized geophysical KdV equation with Coriolis effect
(Elsevier, 2023) Saifullah, Sayed; Baleanu, Dumitru; Fatima, Nahid; Abdelmohsen, Shaimaa A. M.; Alanazi, Meznah M.; Ahmad, Shabir; Baleanu, Dumitru; 56389; Matematik
In this manuscript, we study new solutions of generalized version of geophysical KdV equation which is called generalized perturbed KdV (gpKdV) under time-space conformable oper-ator. We implement two methods to get some novel waves solution of the gpKdV equation. First, we use extended Tanh-method to extract new solutions of considered equations in the form of trigonometric hyperbolic functions. To achieve Sine and Cosine hyperbolic solutions, we use gen-eralized Kudryashov (GK) technique with Riccati equation. We show the behaviour of solutions via 2D and 3D figures. Also, we analyze the Corioles effect on the evolution of waves solutions of the considered equation.CO 2023 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 43
Citation - Scopus: 47
Analysis of the fractional tumour-immune-vitamins model with Mittag-Leffler kernel
(Elsevier, 2020) Ahmad, Shabir; Baleanu, Dumitru; Ullah, Aman; Akgul, Ali; Baleanu, Dumitru; 56389; Matematik
Recently, Atangana-Baleanu fractional derivative has got much attention of the researchers due to its nonlocality and non-singularity. This operator contains an accurate kernel that describes the better dynamics of systems with a memory effect. In this paper, we investigate the fractional-order tumour-immune-vitamin model (TIVM) under Mittag-Leffler derivative. The existence of at least one solution and a unique solution has discussed through fixed point results. We established the Hyres-Ulam stability of the proposed model under the Mittag-Leffler derivative. The fractional Adams-Bashforth method has used to achieve numerical results. Finally, we simulate the obtained numerical results for different fractional orders to show the effect of vitamin intervention on decreased tumour cell growth and cancer risk. At the end of the paper, the conclusion has provided.
Citation - WoS: 21
Citation - Scopus: 25
Dynamics of Fractional Order Delay Model of Coronavirus Disease
(Amer inst Mathematical Sciences-aims, 2022) Jarad, Fahd; Rahman, Mati Ur; Ahmad, Shabir; Riaz, Muhammad Bilal; Jarad, Fahd; Matematik
The majority of infectious illnesses, such as HIV/AIDS, Hepatitis, and coronavirus (2019-nCov), are extremely dangerous. Due to the trial version of the vaccine and different forms of 2019-nCov like beta, gamma, delta throughout the world, still, there is no control on the transmission of coronavirus. Delay factors such as social distance, quarantine, immigration limitations, holiday extensions, hospitalizations, and isolation are being utilized as essential strategies to manage the outbreak of 2019-nCov. The effect of time delay on coronavirus disease transmission is explored using a non-linear fractional order in the Caputo sense in this paper. The existence theory of the model is investigated to ensure that it has at least one and unique solution. The Ulam-Hyres (UH) stability of the considered model is demonstrated to illustrate that the stated model's solution is stable. To determine the approximate solution of the suggested model, an efficient and reliable numerical approach (Adams-Bashforth) is utilized. Simulations are used to visualize the numerical data in order to understand the behavior of the different classes of the investigated model. The effects of time delay on dynamics of coronavirus transmission are shown through numerical simulations via MATLAB-17.
Citation - WoS: 17
Citation - Scopus: 18
Fractional Order Mathematical Model of Serial Killing with Different Choices of Control Strategy
(Mdpi, 2022) Rahman, Mati Ur; Jarad, Fahd; Ahmad, Shabir; Arfan, Muhammad; Akgul, Ali; Jarad, Fahd; 234808; Matematik
The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag-Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam's stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.
Citation - WoS: 32
Citation - Scopus: 31
Multiple bifurcation solitons, lumps and rogue waves solutions of a generalized perturbed KdV equation
(Springer, 2023) Khan, Arshad; Baleanu, Dumitru; Saifullah, Sayed; Ahmad, Shabir; Khan, Javed; Baleanu, Dumitru; 56389; Matematik
The perturbed KdV equation has many applications in mechanics and sound propagation in fluids. The aim of this manuscript is to study novel crucial exact solutions of the generalized perturbed KdV equation. The Hirota bilinear technique is implemented to derive general form solution of the considered equation. The novel soliton solutions are studied by taking different dispersion coefficients. We analyse first- and second-order soliton solutions, multiple-bifurcated soliton solutions, first- and second-order lump and rogue wave solutions of the considered equations. We show the effect of the parameters on the evolution of soliton solutions of the considered equation. All the obtained results are simulated by using MATLAB-2020.
Citation - WoS: 2
Citation - Scopus: 2
NUMERICAL ANALYSIS FOR HIDDEN CHAOTIC BEHAVIOR OF A COUPLED MEMRISTIVE DYNAMICAL SYSTEM VIA FRACTAL-FRACTIONAL OPERATOR BASED ON NEWTON POLYNOMIAL INTERPOLATION
(World Scientific Publ Co Pte Ltd, 2023) Abdelmohsen, Shaimaa A. M.; Jarad, Fahd; Ahmad, Shabir; Yassen, Mansour F.; Asiri, Saeed Ahmed; Ashraf, Abdelbacki M. M.; Saifullah, Sayed; Jarad, Fahd; 234808; Matematik
Dynamical features of a coupled memristive chaotic system have been studied using a fractal-fractional derivative in the sense of Atangana-Baleanu. Dissipation, Poincare section, phase portraits, and time-series behaviors are all examined. The dissipation property shows that the suggested system is dissipative as long as the parameter g > 0. Similarly, from the Poincare section it is observed that, lowering the value of the fractal dimension, an asymmetric attractor emerges in the system. In addition, fixed point notions are used to analyze the existence and uniqueness of the solution from a fractal-fractional perspective. Numerical analysis using the Adams-Bashforth method which is based on Newton's Polynomial Interpolation is performed. Furthermore, multiple projections of the system with different fractional orders and fractal dimensions are quantitatively demonstrated, revealing new characteristics in the proposed model. The coupled memristive system exhibits certain novel, strange attractors and behaviors that are not observable by the local operators.
Citation - WoS: 41
Citation - Scopus: 44
Oscillatory and complex behaviour of caputo-fabrizio fractional order hiv-1 infection model
(Amer inst Mathematical Sciences-aims, 2022) Ahmad, Shabir; Jarad, Fahd; Ullah, Aman; Partohaghighi, Mohammad; Saifullah, Sayed; Akgul, Ali; Jarad, Fahd; 234808; Matematik
HIV-1 infection is a dangerous diseases like Cancer, AIDS, etc. Many mathematical models have been introduced in the literature, which are investigated with different approaches. In this article, we generalize the HIV-1 model through nonsingular fractional operator. The non-integer mathematical model of HIV-1 infection under the Caputo-Fabrizio derivative is presented in this paper. The concept of Picard-Lindelof and fixed-point theory are used to address the existence of a unique solution to the HIV-1 model under the suggested operator. Also, the stability of the suggested model is proved through the Picard iteration and fixed point theory approach. The model's approximate solution is constructed through three steps Adams-Bashforth numerical method. Numerical simulations are provided for different values of fractional-order to study the complex dynamics of the model. Lastly, we provide the oscillatory and chaotic behavior of the proposed model for various fractional orders.
Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation
(2023) Baleanu, Dumitru; Alqarni, M.M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E.; 56389; Matematik
We investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct a comprehensive analysis, we employ the Generalized Kudryashov Technique (KT), Modified KT, and the sine–cosine method. Through the application of these advanced methods, a diverse range of traveling wave solutions is derived, encompassing both bounded and singular types. Among these solutions are dark and bell-shaped waves, as well as periodic waves. Significantly, our investigation reveals novel solutions that have not been previously documented in existing literature. These findings present novel contributions to the field and offer potential applications in various physical phenomena, enhancing our understanding of nonlinear wave equations.
Citation - WoS: 13
Citation - Scopus: 15
Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation
(Elsevier, 2023) Saifullah, Sayed; Baleanu, Dumitru; Alqarni, M. M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E.; 56389; Matematik
We investigate a generalized scale-invariant analogue of the Korteweg-de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct a comprehensive analysis, we employ the Generalized Kudryashov Technique (KT), Modified KT, and the sine-cosine method. Through the application of these advanced methods, a diverse range of traveling wave solutions is derived, encompassing both bounded and singular types. Among these solutions are dark and bell-shaped waves, as well as periodic waves. Significantly, our investigation reveals novel solutions that have not been previously documented in existing literature. These findings present novel contributions to the field and offer potential applications in various physical phenomena, enhancing our understanding of nonlinear wave equations.
Citation - WoS: 14
Citation - Scopus: 15
Study On The Dynamics Of A Pıecewise Tumor-Immune Interaction Model
(World Scientific Publ Co Pte Ltd, 2022) Saifullah, Sayed; Jarad, Fahd; Ahmad, Shabir; Jarad, Fahd; 234808; Matematik
Many approaches have been proposed in recent decades to represent the behaviors of certain complicated global problems appearing in a variety of academic domains. One of these issues is the multi-step behavior that some situations exhibit. Abdon and Seda devised new operators known as "piecewise operators" to deal with such problems. This paper presents the dynamics of the tumor-immune-vitamins model in the sense of a piecewise derivative. The piecewise operator considered here is composed of classical and Caputo operators. The existence and uniqueness of the solution with a piecewise derivative are presented with the aid of fixed point results. With the help of the Newton polynomial, a numerical scheme is presented for the examined model. The attained results are visualized through simulations for different fractional orders.
Citation - WoS: 28
Citation - Scopus: 31
Theoretical and Numerical Analysis of Fractal Fractional Model of Tumor-Immune Interaction With Two Different Kernels
(Elsevier, 2022) Baleanu, Dumitru; Ullah, Aman; Akgu, Ali; Baleanu, Dumitru; Matematik
Fractal fractional operators in Caputo and Caputo-Fabrizio sense are being used in this manuscript to explore the interaction between the immune system and cancer cells. The tumour-immune model has been investigated numerically and theoretically by the singular and nonsingular fractal fractional operators. Via fixed point theorems, the existence and uniqueness of the model under the Caputo fractal fractional operator have been demonstrated. Using the fixed point theory, the existence of a unique solution has been derived under the Caputo-Fabrizio case. Through nonlinear analysis, the Ulam-Hyres stability of the model has been derived. For the singular and nonsingular fractal fractional operators, numerical results have been developed by Lagrangian-piece wise interpolation. We simulate the numerical results for the various sets of fractional and fractal orders to describe the relationship between immune and cancer cells under the novel operators with two different kernels. We compared the dynamics of the tumor-immune model using a power law and an exponential-decay kernel to explore that the nonsingular fractal fractional operator provides better dynamics for the considered model. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University