Abstract
In this paper, we provide approximate solution to linear time-fractional Kline-Gordon equations (FKGEs) with initial conditions by using the residual power series (RPS) method. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. Graphical results show the geometric behaviors to the approximate solutions at different values of fraction order 𝛾. The numerical analysis detects that the RPS technique is an efficient, simple and powerful tool to determine the solutions of the time-fractional KGE.
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