Qualitative Study on ψ−Caputo fractional differential inclusion with non-local conditions and feedback control

Abstract

This article discuss the existence of solutions for certain classes of nonlinear ψ-Caputo fractional derivative differential inclusion via a nonlocal infinite-point or Riemann-Stieltjes integral boundary conditions and with a feedback control in Banach spaces. Our approach is based on Schauder's fixed point theorem. We establish appropriate conditions that guarantee unique solutions and demonstrate that the solution continuously depends on the set of selections and some other functions. Additionally, we include example to illustrate the key findings.