Fractional-Order Investigation of Diffusion Equations via Analytical Approach

Frontiers in Physics

Hassan Khan³  Saima Mustafa⁴  Dumitru Baleanu⁵  Lianming Mou⁶  Haobin Liu⁶ 

[1] Department of Mathematics, Abdul Wali khan University Mardan, Mardan, Pakistan;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey;Department of Mathematics, Near East University TRNC, Mersin, Turkey;Department of Mathematics, Pir Mehr Ali Shah Arid Agriculture University, Rawalpindi, Pakistan;Institute of Space Sciences, Magurele-Bucharest, Romania;School of Mathematics and Information Sciences, Neijiang Normal University, Neijiang, China;

关键词: iterative shehu transform method;    diffusion equations;    caputo operator;    mittag-leffler function;    fractional differential equation;   

DOI  :  10.3389/fphy.2020.568554

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown