Browsing by Author "Ullah, Aman"

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Citation Count: Ahmad, Shabir;...et.al. (2022). "A hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations", AIMS Mathematics, Vol.7, No.5, pp.9389-9404.
A hybrid analytical technique for solving nonlinear fractional order PDEs of power law kernel: Application to KdV and Fornberg-Witham equations
(2022) Ahmad, Shabir; Ullah, Aman; Akgül, Ali; Jarad, Fahd; 234808
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. To 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 Count: Akgül, Ali...et al. (2021). "A novel method for analysing the fractal fractional integrator circuit", Alexandria Engineering Journal, Vol. 60, No. 4, pp. 3721-3729.
A novel method for analysing the fractal fractional integrator circuit
(2021) Akgül, Ali; Ahmad, Shabir; Ullah, Aman; Baleanu, Dumitru; Akgül, Esra Karataş; 56389
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 Count: Ahmad, Shabir...at all (2020). "Analysis of the fractional tumour-immune-vitamins model with Mittag-Leffler kernel", Results in Physics, Vol. 19.
Analysis of the fractional tumour-immune-vitamins model with Mittag-Leffler kernel
(2020) Ahmad, Shabir; Ullah, Aman; Akgül, Ali; Baleanu, Dumitru; 56389
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 Count: Ahmad, Shabir;...et.al. (2022). "Oscillatory and complex behaviour of caputo-fabrizio fractional order hiv-1 infection model", AIMS Mathematics, Vol.7, No.3, pp.4778-4792.
Oscillatory and complex behaviour of caputo-fabrizio fractional order hiv-1 infection model
(2022) Ahmad, Shabir; Ullah, Aman; Partohaghighi, Mohammad; Saifullah, Sayed; Akgül, Ali; Jarad, Fahd; 234808
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 Count: Din, Rahim ud...et al. (2020). "Study of global dynamics of COVID-19 via a new mathematical model", Results in Physics, Vol. 19.
Study of global dynamics of COVID-19 via a new mathematical model
(2020) Din, Rahim ud; Seadawy, Aly R.; Shah, Kamal; Ullah, Aman; Baleanu, Dumitru; 56389
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.