Applied Mathematics & Information Sciences

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This paper presents an innovative approach to solve equal-width time-fractional-order equations that describe the behavior of waves in a certain physical system, using the Caputo operator to express the fractional derivative by improving the Taylor series expansion.Its convergence theorem is proven, and the error between the exact and approximate solutions is estimated; the resulting solutions are illustrated using graphs for different values of the fractional derivative order and time.The primary objective of this study is to demonstrate the effectiveness of the method in reducing computational effort for solving nonlinear fractional partial differential equations (NFPDEs).

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