The LaPlace Homotopy analysis method for solving systems of fractional integral differential equations

Abstract

The paper presents the Laplace homotopy analysis method (LHAM) as an efficient
and robust approach to solving systems of fractional integral differential equations
(FIDE). The combination of the Laplace transform and the homotopy analysis
method (HAM) solves the convergence and computational problems that often occur
when solving fractional systems. By transforming differential equations into
algebraic ones, LHAM increases the ease of working with partial derivatives while
maintaining flexibility and stability using auxiliary parameters. The paper
demonstrates the effectiveness of LHAM through examples, comparing its
performance with established methods such as the Adomian Decomposition Method
(ADM) and the Variational Iteration Method (VIM), showing its superior accuracy
and efficiency.