Malaysian Journal of Mathematical Sciences, September 2024, Vol. 18, No. 3
Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space
Alsa'di, K., Nik Long, N. M. A., and Eshkuvatov, Z. K.
Corresponding Email: [email protected]
Received date: 4 December 2022
Accepted date: 4 March 2024
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.
Keywords: Caputo fractional derivative; Hyers-Ulam stability; Laplace Adomian decomposition method
