Approximate Solution of Nonlinear Time-Fractional PDEs by Laplace Residual Power Series Method

Most physical phenomena are formulated in the form of non-linear fractional partial differential equations to better understand complexity these phenomena. This article introduces a recent attractive analytic-numeric approach investigate approximate solutions for nonlinear time by means coupling Laplace transform operator and Taylor’s formula. The validity applicability used method illustrated via solving time-fractional Kolmogorov Rosenau–Hyman models with appropriate initial data. series both produced rapid convergence McLaurin based upon limit concept fewer computations more accuracy. Graphs two three dimensions drawn detect effect time-Caputo derivatives on behavior obtained results aforementioned models. Comparative point out accurate approximation proposed compared existing methods such as variational iteration homotopy perturbation method. outcomes revealed that is simple, applicable, convenient scheme understanding variety