Abstract
The Asymptotic Homotopy Perturbation Transform Method AHPTM is presented in this work. It is combined version of the Asymptotic Homotopy Perturbation Method AHPM and Laplace transformation. The focus of the work is the introduction of a new fast convergent scheme to obtain the solution of the fractional partial differential equations. Therefore, the first demonstration of the AHPTM is present for the solution of space-fractional telegraph equation (SFTE) in this work. The Caputo version of fractional derivatives has been utilized. Three test problems of the important fractional telegraph model were solved by this proposed scheme. The scheme of AHPTM worked without exploiting Ji. Huan He polynomials or Adomian polynomials. This application was elaborated by providing error estimates, a graphical presentation and tabulation of the results obtained by AHPTM. The comparison of results obtained by AHPTM with exact results is provided which indicated the accuracy of the scheme.
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