Monotone Iterative and Upper-Lower Solution Techniques for Solving the Nonlinear psi-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 psi-Caputo derivative CDa+sigma;psi rho(t)=V(t,rho(t)) under integral boundary conditions rho(a)=lambda I nu;psi rho(eta)+delta. 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 psi*(t) as t, Caputo, 2t, t, and Katugampola (for rho=0.5) derivatives and examine the validity of the acquired outcomes with the help of two different particular examples.