Existence and Uniqueness of Solutions for Fractional Neutral Volterra-Fredholm Integro Differential Equations

The topic fractional calculus can be measured as an old as well as a new subject. In the fractional calculus the various integral inequalities plays an important role in the study of qualitative and quantitative properties of solution of differential and integral equations. In this paper, we study the existence and uniqueness of solutions for the neutral Caputo fractional Volterra-Fredholm integro differential equations with fractional integral boundary conditions by means of the Arzela-Ascoli's theorem, Leray-Schauder nonlinear alternative and the Krasnoselskii fixed point theorem. New conditions on the nonlinear terms are given to pledge the equivalence. An example is provided to illustrate the results.