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

Mona Alsulami (), Mariam Al-Mazmumy, Maryam Ahmed Alyami and Asrar Saleh Alsulami
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Mona Alsulami: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Mariam Al-Mazmumy: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Maryam Ahmed Alyami: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia
Asrar Saleh Alsulami: Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia

Mathematics, 2024, vol. 12, issue 22, 1-16

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.

Keywords: ? -Caputo derivative; generalized Laplace transform; initial value problem; Adomian decomposition method; pharmacokinetics model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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