Monotone Iterative and Upper–Lower Solution Techniques for Solving the Nonlinear ψ−Caputo Fractional Boundary Value Problem

Abstract

The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the ψ−Caputo derivative CDa+σ;ψϱ(t)=V(t,ϱ(t)) under integral boundary conditions ϱ(a)=λIν;ψϱ(η)+δ. Our main results are obtained by applying the monotone iterative technique combined with the method of upper and lower solutions. Further, we consider three cases for ψ*(t) as t, Caputo, 2t, t, and Katugampola (for ρ=0.5) derivatives and examine the validity of the acquired outcomes with the help of two different particular examples.