Browsing by Author "Ullah, Aman"

Now showing 1 - 7 of 7

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: 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: 6
Citation - Scopus: 9
Computation of semi-analytical solutions of fuzzy nonlinear integral equations
(Springer, 2020) Ullah, Zia; Baleanu, Dumitru; Ullah, Aman; Shah, Kamal; Baleanu, Dumitru; 56389; Matematik
In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A hybrid method of Laplace transform coupled with Adomian decomposition method is used to find the solution of the fuzzy nonlinear integral equations including fuzzy nonlinear Fredholm integral equation, fuzzy nonlinear Volterra integral equation, and fuzzy nonlinear singular integral equation of Abel type kernel. We also provide some suitable examples to better understand the proposed method.
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.
Citation - WoS: 33
Citation - Scopus: 39
Study of global dynamics of COVID-19 via a new mathematical model
(Elsevier, 2020) Din, Rahim Ud; Baleanu, Dumitru; Seadawy, Aly R.; Shah, Kamal; Ullah, Aman; Baleanu, Dumitru; 56389; Matematik
The theme of this paper focuses on the mathematical modeling and transmission mechanism of the new Coronavirus shortly noted as (COVID-19), endangering the lives of people and causing a great menace to the world recently. We used a new type epidemic model composed on four compartments that is susceptible, exposed, infected and recovered (SEIR), which describes the dynamics of COVID-19 under convex incidence rate. We simulate the results by using nonstandard finite difference method (NSFDS) which is a powerful numerical tool. We describe the new model on some random data and then by the available data of a particular regions of Subcontinents.
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