Solvability of triple-point integral boundary value problems for a class of impulsive fractional differential equations

Kaihong Zhao,Jiangyan Liang

doi:10.1186/s13662-017-1099-0

Abstract

This paper is concerned with a class of triple-point integral boundary value problems for impulsive fractional differential equations involving the Riemann-Liouville fractional derivative of order α (2<alphaleq3). Some sufficient criteria for the existence of solutions are obtained by applying the contraction mapping principle and the fixed point theorem. As an application, one example is given to demonstrate the validity of our main results.

Highlights

Towards the end of the th century Liouville and Riemann mentioned the definition of the fractional derivative which is the generalization of the traditional integer order differential and integral calculus
The boundary value problems of fractional differential equations have received a great deal of attention
There are a large number of papers dealing with the existence, nonexistence, multiplicity of solutions of boundary value problem for some nonlinear fractional differential equations

Summary

Introduction

Towards the end of the th century Liouville and Riemann mentioned the definition of the fractional derivative which is the generalization of the traditional integer order differential and integral calculus. The boundary value problems of fractional differential equations have received a great deal of attention. There are a large number of papers dealing with the existence, nonexistence, multiplicity of solutions of boundary value problem for some nonlinear fractional differential equations (see [ – ]). The boundary value problems of impulsive fractional differential equations have been studied extensively in the literature (see [ – ]). We will study the existence and uniqueness of solutions for the following impulsive integral boundary value problems (BVPs for short) of fractional order differential equations:. In Section , we give some sufficient conditions for the existence of single positive solutions for boundary value problem

Preliminaries

Illustrative example

Conclusions