On the existence and uniqueness of solutions to a new class of fractional boundary value problems

Abstract

In this article, we verify the existence and uniqueness of solution for a class of nonlinear boundary value problem for fractional differential equation of order $3<\alpha \le 4$, with the standard fractional derivative in the sense of Riemann–Liouville. By using a variety of tools including the Schauder fixed-point theorem, the Krasnoseĺskii fixed-point theorem and contraction mapping principle, existence and uniqueness results are obtained. Some examples are given to expression the results.

Keywords:

• fractional differential equations
• boundary value problem
• fixed-point theorem
• existencesolution
• contraction principle

2010 AMS Subject Classifications:

• 26A33
• 34A08
• 34A12

Disclosure statement

No potential conflict of interest was reported by the authors.