Browsing by Author "Liu, Haobin"

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Citation Count: Liu, Haobin...et al. (2021). "Fractional-Order Investigation of Diffusion Equations via Analytical Approach", Frontiers in Physics, Vol. 8.
Fractional-Order Investigation of Diffusion Equations via Analytical Approach
(2021) Liu, Haobin; Khan, Hassan; Mustafa, Saima; Mou, Lianming; Baleanu, Dumitru; 56389
This research article is mainly concerned with the analytical solution of diffusion equations within a Caputo fractional-order derivative. The motivation and novelty behind the present work are the application of a sophisticated and straight forward procedure to solve diffusion equations containing a derivative of a fractional-order. The solutions of some illustrative examples are calculated to confirm the closed contact between the actual and the approximate solutions of the targeted problems. Through analysis it is shown that the proposed solution has a higher rate of convergence and provides a closed-form solution. The small number of calculations is the main advantage of the proposed method. Due to a comfortable and straight forward implementation, the suggested method can be utilized to nonlinear fractional-order problems in various applied science branches. It can be extended to solve other physical problems of fractional-order in multiple areas of applied sciences. © Copyright © 2021 Liu, Khan, Mustafa, Mou and Baleanu.
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.