Next Article in Journal
A New Quantum Blind Signature Scheme with BB84-State
Next Article in Special Issue
New Texture Descriptor Based on Modified Fractional Entropy for Digital Image Splicing Forgery Detection
Previous Article in Journal
Using Minimum Local Distortion to Hide Decision Tree Rules
Previous Article in Special Issue
A Fractional-Order Partially Non-Linear Model of a Laboratory Prototype of Hydraulic Canal System
Article Menu

Export Article

Open AccessArticle
Entropy 2019, 21(4), 335; https://doi.org/10.3390/e21040335

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

1,†, 1,†, 1,† and 2,3,*,†
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
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 22 February 2019 / Revised: 17 March 2019 / Accepted: 24 March 2019 / Published: 28 March 2019
(This article belongs to the Special Issue The Fractional View of Complexity)
  |  
PDF [1175 KB, uploaded 28 March 2019]
  |     |  

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

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Shah, R.; Khan, H.; Arif, M.; Kumam, P. Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations. Entropy 2019, 21, 335.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top