The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the $\mathsf{\psi }-$Caputo derivative ${}^C{\mathbb{D}}_{a^{+}}^{\sigma ;\mathsf{\psi }}\varrho \left(\mathrm{t}\right)=\mathcal{V}(\mathrm{t},\varrho \left(\mathrm{t}\right))$ under integral boundary conditions $\varrho \left(a\right)=\lambda {\mathbb{I}}^{\nu ;\mathsf{\psi }}\varrho \left(\eta \right)+\delta$. 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 ${\mathsf{\psi }}^{*}\left(\mathrm{t}\right)$ as $\mathrm{t}$, Caputo, $2^{\mathrm{t}}$, $\sqrt{\mathrm{t}}$, and Katugampola (for $\rho =0.5)$ derivatives and examine the validity of the acquired outcomes with the help of two different particular examples.

This paper concerned with study the existence and uniqueness of solutions for a class of fractional differential equations with boundary conditions involving the Riesz-Caputo type fractional derivatives. We apply the methods of functional analysis such that the uniqueness result is established using the Banach contraction principle, whereas existence results are obtained using Schaefer's and Krasnoslkii's fixed theorems. Some examples are given to illustrate our acquired results.

In this work, we present some results on the existence of attractive solutions of fractional differential equations of the ѱ-Hilfer hybrid type. The results on the existence of solutions are a consequence of the Schauder fixed point theorem. Next, we prove that all solutions are uniformly locally attractive.

The aim of this work is to study the existence of solutions to a class of fractional differential equations with a mixed of fractional integral boundary conditions involving the Hilfer fractional derivative. The proof is based on Monch's fixed point theorem and the technique of measures of noncompactness. Two examples illustrating the main results are also constructed.