- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 4 Issue: 4
- Existence and Uniqueness Results for Volterra-Fredholm Integro Differential Equations
Existence and Uniqueness Results for Volterra-Fredholm Integro Differential Equations
Authors : Ahmed HAMOUD, Nedal MOHAMMED, Kirtiwant GHADLE
Pages : 361-372
Doi:10.31197/atnaa.703984
View : 7 | Download : 2
Publication Date : 2020-12-30
Article Type : Research
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