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# Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method

by 2,3, 4,5,* and
1
Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
2
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
3
Institute of Space Sciences, Magurele-Bucharest 077125, Romania
4
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
5
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Electronics 2019, 8(9), 1015; https://doi.org/10.3390/electronics8091015
Received: 15 July 2019 / Revised: 13 August 2019 / Accepted: 21 August 2019 / Published: 11 September 2019
In the current paper, fractional-order hyperbolic telegraph equations are considered for analytical solutions, using the decomposition method based on natural transformation. The fractional derivative is defined by the Caputo operator. The present technique is implemented for both fractional- and integer-order equations, showing that the current technique is an accurate analytical instrument for the solution of partial differential equations of fractional-order arising in all branches of applied sciences. For this purpose, several examples related to hyperbolic telegraph models are presented to explain the procedure of the suggested method. It is noted that the procedure of the present technique is simple, straightforward, accurate, and found to be a better mathematical technique to solve non-linear fractional partial differential equations. View Full-Text
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Khan, H.; Shah, R.; Baleanu, D.; Kumam, P.; Arif, M. Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method. Electronics 2019, 8, 1015.