Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique

Frontiers in Physics

Hassan Khan²  Muhammad Arif²  Rasool Shah²  Umar Farooq²  Poom Kumam⁴  Dumitru Baleanu⁵ 

[1] Center of Excellence in Theoretical and Computational Science (TaCS-CoE) and KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, Thailand;Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Pakistan;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Institute of Space Sciences, Măgurele, Romania;

关键词: analytical solution;    Mohand transform;    Adomian decomposition;    caputo derivatives;    third order Kortewege-De Vries equations;   

DOI  :  10.3389/fphy.2019.00244

来源: DOAJ

【 摘 要 】

In the present article, fractional view of third order Kortewege-De Vries equations is presented by a sophisticated analytical technique called Mohand decomposition method. The Caputo fractional derivative operator is used to express fractional derivatives, containing in the targeted problems. Some numerical examples are presented to show the effectiveness of the method for both fractional and integer order problems. From the table, it is investigated that the proposed method has the same rate of convergence as compare to homotopy perturbation transform method. The solution graphs have confirmed the best agreement with the exact solutions of the problems and also revealed that if the sequence of fractional-orders is approaches to integer order, then the fractional order solutions of the problems are converge to an integer order solution. Moreover, the proposed method is straight forward and easy to implement and therefore can be used for other non-linear fractional-order partial differential equations.

【 授权许可】

Unknown