Existence and Uniqueness of Continuous Solutions for Conformable Fractional Integro-Differential Equations in Cone Metric Spaces

Abstract

In this paper, by the application of some extensions of Banach's contraction principle in complete cone metric space, we have proved the existence and uniqueness of solutions to fractional order integro-differential equations of Volterra-Fredholm type which are defined in a cone metric space. The fractional order derivative defined in the integro-differential equation is the conformable fractional order derivative. The obtained results are used for solving a couple of fractional order integro-differential equations of Volterra-Fredholm type.

Mathematics Subject Classification: 34B05.