Browsing by Author "Alderremy, A. A."

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Citation Count: Liu, Haobin...et al. (2020). "On the Fractional View Analysis of Keller-Segel Equations with Sensitivity Functions", Complexity, Vol. 2020.
On the Fractional View Analysis of Keller-Segel Equations with Sensitivity Functions
(2020) Liu, Haobin; Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; 56389
In this paper, the fractional view analysis of the Keller-Segal equations with sensitivity functions is presented. The Caputo operator has been used to pursue the present research work. The natural transform is combined with the homotopy perturbation method, and a new scheme for implementation is derived. The modified established method is named as the homotopy perturbation transform technique. The derived results are compared with the solution of the Laplace Adomian decomposition technique by using the systems of fractional Keller-Segal equations. The solution graphs and the table have shown that the obtained results coincide with the solution of the Laplace Adomian decomposition method. Fractional-order solutions are determined to confirm the reliability of the current method. It is observed that the solutions at various fractional orders are convergent to an integer-order solution of the problems. The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.
Citation Count: Xu, Jiabin...et al (2021). "The analytical analysis of nonlinear fractional-order dynamical models", AIMS Mathematics, Vol. 6, No. 6, pp. 6201-6219.
The analytical analysis of nonlinear fractional-order dynamical models
(2021) Xu, Jiabin; Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Baleanu, Dumitru; 56389
The present research paper is related to the analytical solution of fractional-order nonlinear Swift-Hohenberg equations using an efficient technique. The presented model is related to the temperature and thermal convection of fluid dynamics which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In this work Laplace Adomian decomposition method is implemented because it require small volume of calculations. Unlike the variational iteration method and Homotopy pertubation method, the suggested technique required no variational parameter and having simple calculation of fractional derivative respectively. Numerical examples verify the validity of the suggested method. It is confirmed that the present method's solutions are in close contact with the solutions of other existing methods. It is also investigated through graphs and tables that the suggested method's solutions are almost identical with different analytical methods.
Citation Count: Alderremy, A. A...et al. (2020). "The Analytical Analysis of Time-Fractional Fornberg-Whitham Equations", Mathematics, Vol. 8, No. 6.
The Analytical Analysis of Time-Fractional Fornberg-Whitham Equations
(2020) Alderremy, A. A.; Khan, Hassan; Shah, Rasool; Aly, Shaban; Baleanu, Dumitru; 56389
This article is dealing with the analytical solution of Fornberg-Whitham equations in fractional view of Caputo operator. The effective method among the analytical techniques, natural transform decomposition method, is implemented to handle the solutions of the proposed problems. The approximate analytical solutions of nonlinear numerical problems are determined to confirm the validity of the suggested technique. The solution of the fractional-order problems are investigated for the suggested mathematical models. The solutions-graphs are then plotted to understand the effectiveness of fractional-order mathematical modeling over integer-order modeling. It is observed that the derived solutions have a closed resemblance with the actual solutions. Moreover, using fractional-order modeling various dynamics can be analyzed which can provide sophisticated information about physical phenomena. The simple and straight-forward procedure of the suggested technique is the preferable point and thus can be used to solve other nonlinear fractional problems.