Bicomplex Laplace Adomian Approach for ψ-Caputo Fractional Differential Equations

Abstract

n this work, we propose the ψ-Bicomplex Laplace Transform Adomian Decomposition Method to solve fractional differential e quations d efined wi th re spect to a fu nction ψ in the Caputo sense. This approach integrates the effective Adomian Decomposition Method with a generalized form of the classical bicomplex Laplace transform. We apply the resulting recursive scheme to several numerical examples, including a real-world pharmacokinetic model describing drug concentration in human blood, to evaluate the method’s performance. The solutions obtained closely align with known analytical results, while the pharmacokinetic model outcomes closely match experimental data. These findings d emonstrate t he r eliability a nd e ffectiveness of the method in solving a broad class of ψ-fractional differential equations.