Novel results of weak solutions for fractional integrodifferential equations involving Gronwall inequality in Banach spaces

Abstract

We study the boundary value problems for fractional integrodifferential equations involving Caputo derivative in Banach spaces. A priori bounds are obtained by using generalized singular type Gronwall inequality. Sufficient condition for the existence of solutions are proven by integrity of fractional calculus and fixed-point method under some mild conditions. Finally, the results are exhibited by an example.