Applied Mathematics & Information Sciences

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In this paper, the time-fractional nonlinear Kline-Gordon equations are considered and solved using the adaptive of residual power series method. The fractional derivative is considered in a conformable sense. Analytical solutions are obtained based on conformable Taylor series expansion by substituting the truncated conformable series solutions to residual error functions. This adaptation can be implemented as a novel alternative technique to handle many nonlinear issues occurring in physics and engineering. Effectiveness, validity, and feasibility of the proposed method are demonstrated by testing some numerical applications. Tabular and graphic results indicate that the method is superior, accurate and appropriate for solving these fractional partial differential models with compatible derivatives.

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