Controllability of a Class of Impulsive ψ-Caputo Fractional Evolution Equations of Sobolev Type

Abstract

In this paper, we investigate the controllability of a class of impulsive ψ-Caputo fractional evolution equations of Sobolev type in Banach spaces. Sufficient conditions are presented by two new characteristic solution operators, fractional calculus, and Schauder fixed point theorem. Our works are generalizations and continuations of the recent results about controllability of a class of impulsive ψ-Caputo fractional evolution equations. Finally, an example is given to illustrate the effectiveness of the main results.

Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps

“…So, the averaging principle for the ψ-Capuo FSDDE with Poisson jumps is successfully established. 31) and (32) with α = 0.9 and ε = 0.01.…”

“…In [28], Almeida generalized the definition of the Caputo fractional derivative by considering the Caputo fractional derivative of a function with respect to another function ψ. Since then, there have been so many papers involving the ψ-Caputo fractional derivative, see [29][30][31][32]. Recently, there have been many works on SDEs with Poisson jumps, see, for example, [33][34][35] and the references therein.…”