Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space
Year: 2024
Type: article
Abstract: This paper examines the theoretical, analytical, and approximate solutions of the Caputo fractional Volterra-Fredholm integro-differential equations (FVFIDEs). Utilizing Schaefer's fixed-point theorem, the Banach contraction theorem and the Arzel\`{a}-Ascoli theorem, we establish some conditions that guarantee the existence and uniqueness of the solution. Furthermore, the stability of the solution is proved using the Hyers-Ulam stability and Gronwall-Bellman's inequality. Additionally, the Laplace Adomian decomposition method (LADM) is employed to obtain the approximate solutions for both linear and non-linear FVFIDEs. The method's efficiency is demonstrated through some numerical examples.
Institutions: Universiti Putra Malaysia, Universiti Malaysia Terengganu
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403044047