Work

Generalized Laplace Transform with Adomian Decomposition Method for Solving Fractional Differential Equations Involving ψ-Caputo Derivative

Year: 2024

Type: article

Abstract: In this study, we introduced the ψ-Laplace transform Adomian decomposition method, which is a combination of the efficient Adomian decomposition method with the generalization of the classical Laplace transform to treat fractional differential equations with respect to another function, ψ, in the Caputo sense. To validate the effectiveness of this method, we applied the derived recurrent scheme of the ψ-Laplace Adomian decomposition on several test numerical problems, including a real-life scenario in pharmacokinetics that models the movement of drug concentration in human blood. The solutions obtained closely matched the known solutions for the test problems. Additionally, in the pharmacokinetics case, the results were consistent with the available physical data. Consequently, this method simplifies the verification of numerous related aspects and proves advantageous in solving various ψ-fractional differential equations.

Source: Mathematics

DOI: 10.3390/math12223499

Authors: Mona Alsulami, Mariam Al-Mazmumy, Maryam Ahmed Alyami, Asrar Saleh Alsulami

Institution: University of Jeddah

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: University of Jeddah