A New Class of ψ -Caputo Fractional Differential Equations and Inclusion

Abstract

In the present research work, we investigate the existence of a solution for new boundary value problems involving fractional differential equations with $\psi$ -Caputo fractional derivative supplemented with nonlocal multipoint, Riemann–Stieltjes integral and $\psi$ -Riemann–Liouville fractional integral operator of order $\gamma$ boundary conditions. Also, we study the existence result for the inclusion case. Our results are based on the modern tools of the fixed-point theory. To illustrate our results, we provide examples.