Browsing by Author "Mustafa, Saima"

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Citation Count: Khan, Hassan...et al. (2020). "Approximate analytical fractional view of convection-diffusion equations", Open Physics, Vol. 18, No. 1, pp. 897-905.
Approximate analytical fractional view of convection-diffusion equations
(2020) Khan, Hassan; Mustafa, Saima; Ali, Izaz; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; 56389
In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection-diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.
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.