Existence and Uniqueness Results for Volterra-Fredholm Integro Differential Equations

Year 2020, Volume: 4 Issue: 4, 361 - 372, 30.12.2020

Ahmed Hamoud , Nedal Mohammed Kirtiwant Ghadle

https://doi.org/10.31197/atnaa.703984

Cited By: 9

Abstract

This paper establishes a study on some important latest innovations in the existence and uniqueness results by means of Krasnoselskii's fixed point and the Banach fixed point theorems for Caputo fractional Volterra-Fredholm integro-differential equations with initial condition. New conditions on the nonlinear terms are given to pledge the equivalence. Finally, an illustrative example is also presented. 

Keywords

Caputo fractional derivative, Volterra-Fredholm integro-differential equation, Caputo sense, Gronwall-Bellman's inequality, Banach contraction fixed point theorem

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