Abstract
In this work, the natural transform decomposition method (NTDM) is applied to solve the linear and nonlinear fractional telegraph equations. This method is a combined form of the natural transform and the Adomian decomposition methods. In addition, we prove the convergence of our method. Finally, three examples have been employed to illustrate the preciseness and effectiveness of the proposed method.
Highlights
The fractional calculus plays an important role in applied mathematics and other fields such as science, physics and engineering
In [1] the fractional telegraph equation is obtained from the classical telegraph equation by replacing the second-order distance derivative with the fractional derivative (0 < α ≤ 2) given to it
The natural transform of Mittag-Leffler function Eα,β is defined as follows
Summary
The fractional calculus (non-integer) plays an important role in applied mathematics and other fields such as science, physics and engineering. It describes the smallest details of natural phenomena, which is better than using a calculus integer. The main aim of this article is to use the (NTDM) to obtain the approximate solution of linear and nonlinear fractional telegraph equations. Adomian decomposition method is a sturdy mathematical method for solving linear and nonlinear fractional telegraph equation and is an amelioration of the existing methods
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