In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach's fixed point theorem, Leray-Schauder's nonlinear alternative and Leray-Schauder's degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.

This paper studies a coupled system of two differential equations of arbitrary orders using Caputo approach with n derivatives, n ∈ N * , n = 1. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using Schaefer and Krasnoselskii fixed point theorems. Some illustrative examples are also presented.

In this paper, we discuss the existence, uniqueness and stability of solutions for a nonlocal boundary value problem of nonlinear fractional differential equations with two Caputo fractional derivatives. By applying the contraction mapping and O’Regan fixed point theorem, the existence results are obtained. We also derive the Ulam-Hyers stability of solutions. Finally, some examples are given to illustrate our results.

This paper investigates the existence of solutions for a boundary value problem of nonlinear fractional differential equations with nonlocal boundary conditions. We use Banach fixed point theorem to prove an existence and uniqueness result. Then, by using O'Regan fixed point theorem, we prove an existence result. Finally, illustrative examples of our main results are presented.

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