Theoretical and Numerical Studies of Fractional Volterra-Fredholm Integro-Differential Equations in Banach Space
K. Alsa'di,,
N. M. A. Nik Long,
Z. K. Eshkuvatov
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 deco… Show more
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