Existence and uniqueness results of boundary value problems for nonlinear fractional differential equations involving ψ−Caputo-type fractional derivatives Existence and uniqueness results of boundary value problems

Abstract

The main crux of this manuscript is to establish some new sufficient conditions for the existence of solutions to a class of boundary value problem for nonlinear fractional differential equations with ψ−Caputo fractional derivatives of order $\beta\in(2,3)$. The proofs are based on some fixed point theorems and some basic concepts of ψ−fractional analysis. As application, several examples are given to illustrate our theoretical results.