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.