Application of Laplace-Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Rasool Shah; Hassan Khan; Muhammad Arif; Poom Kumam

doi:10.3390/e21040335

Application of Laplace-Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

Entropy (Basel). 2019 Mar 28;21(4):335. doi: 10.3390/e21040335.

Authors

Rasool Shah¹, Hassan Khan¹, Muhammad Arif¹, Poom Kumam^{2

3}

Affiliations

¹ Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan.
² Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand.
³ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan.

Abstract

In the present article, we related the analytical solution of the fractional-order dispersive partial differential equations, using the Laplace-Adomian decomposition method. The Caputo operator is used to define the derivative of fractional-order. Laplace-Adomian decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. The fractional order solutions that are convergent to integer order solutions are also investigated.

Keywords: Caputo operator; Laplace–Adomian decomposition method; analytical solution; third-order dispersive equations.