The study aims to prove the controllability of mild solution for semilinar fractional integerodifferential equations with nonlocal conditions in banach spaces.
 Fractional calculus, compact semigroups and fixed point theorem, are concepts consulted obtain results this work.

Abstract In this paper, we give some basic concepts of q -calculus that will be needed in paper. Then, built the q-nonlocal condition ensures solution existence and uniqueness fractional q-integrodifferential equation. Also, introduce continuous dependence solution. We find numerical using finite-difference-Trapezoidal cubic B-spline-Trapezoidal methods. Finally, three examples to illustrate va...

In this paper, we prove the existence of at least three positive solutions of boundary value problems for nth order nonlinear impulsive integrodifferential equations of mixed type on infinite interval with infinite number of impulsive times. Our results are obtained by applying a new fixed point theorem introduced by Avery and Peterson.