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Open AccessArticle

An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph 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
4
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 426; https://doi.org/10.3390/math7050426
Received: 9 April 2019 / Revised: 30 April 2019 / Accepted: 6 May 2019 / Published: 13 May 2019
In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equations—particularly the fractional-order telegraph equation. View Full-Text
Keywords: Laplace-adomian decomposition method; fractional-order of telegraph equations; Caputo operator Laplace-adomian decomposition method; fractional-order of telegraph equations; Caputo operator
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MDPI and ACS Style

Khan, H.; Shah, R.; Kumam, P.; Baleanu, D.; Arif, M. An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations. Mathematics 2019, 7, 426. https://doi.org/10.3390/math7050426

AMA Style

Khan H, Shah R, Kumam P, Baleanu D, Arif M. An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations. Mathematics. 2019; 7(5):426. https://doi.org/10.3390/math7050426

Chicago/Turabian Style

Khan, Hassan; Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad. 2019. "An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations" Mathematics 7, no. 5: 426. https://doi.org/10.3390/math7050426

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