An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations
1
Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
2
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(6), 505; https://doi.org/10.3390/math7060505
Received: 21 April 2019 / Revised: 9 May 2019 / Accepted: 13 May 2019 / Published: 2 June 2019
(This article belongs to the Special Issue Fractional Differential and Partial Differential Systems with Applications)
The Kortweg–de Vries equations play an important role to model different physical phenomena in nature. In this research article, we have investigated the analytical solution to system of nonlinear fractional Kortweg–de Vries, partial differential equations. The Caputo operator is used to define fractional derivatives. Some illustrative examples are considered to check the validity and accuracy of the proposed method. The obtained results have shown the best agreement with the exact solution for the problems. The solution graphs are in full support to confirm the authenticity of the present method.
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Keywords:
Laplace–Adomian decomposition method; Fractional–order systems of non-linear partial differential equations; Caputo operator; Laplace transformation; Mittag–Leffler function
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MDPI and ACS Style
Shah, R.; Khan, H.; Kumam, P.; Arif, M. An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations. Mathematics 2019, 7, 505. https://doi.org/10.3390/math7060505
AMA Style
Shah R, Khan H, Kumam P, Arif M. An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations. Mathematics. 2019; 7(6):505. https://doi.org/10.3390/math7060505
Chicago/Turabian StyleShah, Rasool; Khan, Hassan; Kumam, Poom; Arif, Muhammad. 2019. "An Analytical Technique to Solve the System of Nonlinear Fractional Partial Differential Equations" Mathematics 7, no. 6: 505. https://doi.org/10.3390/math7060505
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