Solvability of nonlocal boundary value problem for a class of nonlinear fractional differential coupled system with impulses

Kaihong Zhao,Leping Suo

doi:10.1186/s13662-018-1482-5

Abstract

This paper is considered with a class of nonlinear fractional differential coupled system with fractional differential boundary value conditions and impulses. By means of the Banach contraction principle and the Schauder fixed point theorem, some sufficient criteria are established to guarantee the existence of solutions. As applications, some interesting examples are given to illustrate the effectiveness of our main results.

Highlights

The fractional differential system as a mathematical model has been used to describe many phenomena and processes in a lot of fields such as financial mathematics, control theory, physics, chemistry, bioscience, optical and thermal systems, rheology materials and mechanical systems, signal processing and system identification, control and robotics, and so on
Some experimental results show that the fractional order differential model is more accurate than the integer order differential model
Inspired by the above-mentioned issues, the main aim of this paper is to study the existence and uniqueness of solutions to four-point boundary value problem for a class of nonlinear fractional differential coupling system with impulses as follows:

Summary

Introduction

The fractional differential system as a mathematical model has been used to describe many phenomena and processes in a lot of fields such as financial mathematics, control theory, physics, chemistry, bioscience, optical and thermal systems, rheology materials and mechanical systems, signal processing and system identification, control and robotics, and so on. There has been much research on boundary value problems of fractional order differential systems (see [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]). Inspired by the above-mentioned issues, the main aim of this paper is to study the existence and uniqueness of solutions to four-point boundary value problem for a class of nonlinear fractional differential coupling system with impulses as follows:. Theorem 3.1 If the following conditions (A1)-(A3) hold, the boundary value problem (1.1) has a unique solution pair (u∗(t), v∗(t)).

Examples

Conclusions