Browsing by Author "Adel, Waleed"

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Citation Count: Jena, Rajarama Mohan...et al. (2021). "A robust technique based solution of time-fractional seventh-order Sawada-Kotera and Lax's KdV equations", Modern Physics Letters B, Vol. 35, No. 16.
A robust technique based solution of time-fractional seventh-order Sawada-Kotera and Lax's KdV equations
(2021) Jena, Rajarama Mohan; Chakraverty, Snehashish; Baleanu, Dumitru; Adel, Waleed; Rezazadeh, Hadi; 56389
In this paper, the fractional reduced differential transform method (FRDTM) is used to obtain the series solution of time-fractional seventh-order Sawada-Kotera (SSK) and Lax's KdV (LKdV) equations under initial conditions (ICs). Here, the fractional derivatives are considered in the Caputo sense. The results obtained are contrasted with other previous techniques for a specific case, alpha = 1 revealing that the presented solutions agree with the existing solutions. Further, convergence analysis of the present results with an increasing number of terms of the solution and absolute error has also been studied. The behavior of the FRDTM solution and the effects on different values alpha are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated.
Citation Count: Iqbal, Zafar...et al. (2020). "Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission", Chaos Solitons & Fractals, Vol. 134.
Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission
(2020) Iqbal, Zafar; Ahmed, Nauman; Baleanu, Dumitru; Adel, Waleed; Rafiq, Muhammad; Rehman, Muhammad Aziz-ur; Alshomrani, Ali Saleh; 56389
In this article, an integer order nonlinear HIV/AIDS infection model is extended to the non-integer nonlinear model. The Grunwald Letnikov nonstandard finite difference scheme is designed to obtain the numerical solutions. Structure preservence is one of the main advantages of this scheme. Reproductive number R-0 is worked out and its key role in disease dynamics and stability of the system is investigated with the following facts, if R-0 < 1 the disease will be diminished and it will persist in the community for R-0 > 1. On the other hand, it is sought out that system is stable when R-0 < 1 and R-0 > 1 implicates that system is locally asymptotically stable. Positivity and boundedness of the scheme is also proved for the generalized system. Two steady states of the system are computed and verified by computer simulations with the help of some suitable test problem. (C) 2020 Elsevier Ltd. All rights reserved.
Citation Count: Ahmed, Nauman...et al. (2020). "Stability analysis and numerical simulations of spatiotemporal HIV CD4+T cell model with drug therapy", Chaos, Vol. 30, No. 8.
Stability analysis and numerical simulations of spatiotemporal HIV CD4+T cell model with drug therapy
(2020) Ahmed, Nauman; Elsonbaty, Amr; Adel, Waleed; Baleanu, Dumitru; Rafiq, Muhammad; 56389
In this study, an extended spatiotemporal model of a human immunodeficiency virus (HIV) CD4+ T cell with a drug therapy effect is proposed for the numerical investigation. The stability analysis of equilibrium points is carried out for temporal and spatiotemporal cases where stability regions in the space of parameters for each case are acquired. Three numerical techniques are used for the numerical simulations of the proposed HIV reaction-diffusion system. These techniques are the backward Euler, Crank-Nicolson, and a proposed structure preserving an implicit technique. The proposed numerical method sustains all the important characteristics of the proposed HIV model such as positivity of the solution and stability of equilibria, whereas the other two methods have failed to do so. We also prove that the proposed technique is positive, consistent, and Von Neumann stable. The effect of different values for the parameters is investigated through numerical simulations by using the proposed method. The stability of the proposed model of the HIV CD4+ T cell with the drug therapy effect is also analyzed.