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 derivativeC Dσ;ψ a ϱ(t) =+ V (t, ϱ(t)) under integral boundary conditions ϱ(a) = λIν;ψ ϱ(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