An integrated Laplace transform and accelerated Adomian decomposition approach for solving time-fractional nonlinear partial differential equations

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Abstract

This study focuses on the efficient and accurate solution of time-fractional nonlinear partial differential equations (PDEs), which arise in various scientific and engineering applications but are often challenging to solve due to their complexity. We propose a novel method that integrates the Laplace transform with the accelerated Adomian decomposition method (AADM), forming the Laplace transform accelerated Adomian decomposition method (LAADM). The key innovation of this approach lies in its ability to handle the fractional time derivative expressed in the Caputo sense, while enhancing convergence speed and reducing computational effort. The methodology is systematically formulated, and several numerical experiments are conducted to validate its performance. The results demonstrate that LAADM provides highly accurate solutions and exhibits superior efficiency when compared to traditional solution techniques for fractional PDEs.

Keywords

fractional Laplace transform / nonlinear partial fractional differential equations / Laplace transform accelerated Adomian / convergence / error analysis uniqueness / accuracy

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