Existence of mild solutions for nonlocal ψ−Caputo-type fractional evolution equations with nondense domain

Abstract

The main crux of this manuscript is to establish the existence and uniqueness of solutions for nonlocal fractional evolution equations involving ψ−Caputo fractional derivatives of an arbitrary order α ∈ (0, 1) with nondense domain. The mild solutions of our proposed model are constructed by employing generalized ψ−Laplace transform and some new density functions. The proofs are based on Krasnoselskii fixed point theorem and some basic techniques of ψ−fractional calculus. As application, a nontrivial example is given to illustrate our theoritical results.

Keywords

• ψ−fractional integral
• ψ−caputo fractional derivative
• ψ−mild solution
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