Browsing by Author "Sweilam, Nasser H."

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Citation - WoS: 2
Citation - Scopus: 3
Editorial Note on the Special Issue: "fractional Calculus Models for the Dynamics of Complex Systems
(Elsevier, 2021) Kumar, Devendra; Pinto, Carla M. A.; Baleanu, Dumitru; Sweilam, Nasser H.
Citation - WoS: 2
Citation - Scopus: 3
Exact Solutions of the Fractional Time-Derivative Fokker-Planck Equation: a Novel Approach
(Wiley, 2023) Sweilam, Nasser H.; Al-Mekhlafi, Seham M.; Baleanu, Dumitru; Abdel-Gawad, Hamdy I.
In the present article, an approach to find the exact solution of the fractional Fokker-Planck equation (FFPE) is presented. It is based on transforming it to a system of first-order partial differential equation via Hopf transformation, together with implementing the extended unified method. On the other hand, a theorem provides the reduction of the fractional derivatives to non-autonomous ordinary derivative is given. Thus, the FFPE is reduced to non-autonomous classical ones. Some explicit solutions of the classical, fractional time-derivative Fokker-Planck equation are obtained. It is shown that the solution of the Fokker-Planck equation is bi-Gaussian's, which was not found up to date. It is found that high friction coefficient plays a significant role in lowering the standard deviation. Further, it is found that the effect of the presence of the fractional derivative prevails that of the fractal derivative. Here, the most interesting result found is that mixed-Gaussian solution is obtained. It is worthy to mention that the mixture of Gaussian's is a powerful tool in machine learning and also in the distribution of loads in networks. Further, varying the order of the fractional time derivatives results to slight effects in the probability distribution function. Also, it is shown that the mean and mean square of the velocity vary slowly.
Citation - WoS: 50
Citation - Scopus: 64
New Studies for General Fractional Financial Models of Awareness and Trial Advertising Decisions
(Pergamon-elsevier Science Ltd, 2017) Abou Hasan, Muner M.; Baleanu, Dumitru; Sweilam, Nasser H.
In this paper, two numerical techniques are introduced to study numerically the general fractional advertising model. This system describes the flux of the consumers from unaware individuals group to aware or purchased group. The first technique is an asymptotically stable difference scheme, which was structured depending on the nonstandard finite difference method. This scheme preserves the properties of the solutions of the model problem as the positivity and the boundedness. The second technique is the Jacobi-Gauss-Lobatto spectral collocation method which is exponentially accurate. By means of this approach, such problem is reduced to solve a system of nonlinear algebraic equations and are greatly simplified the problem. Numerical comparisons to test the behavior of the used techniques are run out. We conclude from the computational work that: the Jacobi-Gauss-Lobatto spectral collocation method is more accurate whereas the nonstandard finite difference method requires less computational time. (C) 2017 Elsevier Ltd. All rights reserved.