Application of the Laplace-Adomian Decomposition Method to Delay Fractional Partial Differential Equations

Abstract

This paper applies the Laplace-Adomian decomposition method (LADM) to solve a class of delay fractional partial differential equations. The method combines the advantages of the Adomian decomposition method and Laplace transform to efficiently construct series solutions for complex fractional models involving time-delay effects. The proposed approach provides an effective analytical framework that simplifies the solution process and improves computational accuracy. Several test problems are presented to justify the method, including both linear and nonlinear cases. The results demonstrate that LADM can yield exact or highly accurate approximate solutions with only a few iterations. The efficiency and precision of the results obtained are compared with those of other analytical and numerical techniques, demonstrating the superiority of the proposed approach in terms of convergence and accuracy.