Existence results for multi-term fractional differential equations with nonlocal multi-point and multi-strip boundary conditions

Ravi P Agarwal,Bashir Ahmad,Ahmed Alsaedi,Najla Alghamdi,Sotiris K Ntouyas

doi:10.1186/s13662-018-1802-9

Abstract

In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and multi-strip boundary value problems of multi-term fractional differential equations by using standard fixed point theorems. We demonstrate the application of the obtained results with the aid of examples. Some new results are also deduced by fixing the parameters involved in the problem at hand.

Highlights

1 Introduction Multi-term fractional differential equations involve more than one fractional order differential operators and appear in the mathematical models of many real world problems
The topic of boundary value problems of differential equations and inclusions containing more than two fractional order operators needs to be investigated
We introduce and investigate a new boundary value problem of multi-term fractional differential equations supplemented with nonlocal multi-point and multi-strip boundary conditions given by δ2cDα+2 + δ1cDα+1 + δ0cDα x(t) = f t, x(t), 0 < α < 1, 0 < t < 1, (1.1)

Summary

Introduction

Multi-term fractional differential equations involve more than one fractional order differential operators and appear in the mathematical models of many real world problems. We use Krasnoselskii’s fixed point theorem to prove the existence of solutions for the problem (1.1)–(1.2) with δ12 – 4δ0δ2 > 0. 1. In the result, we prove the uniqueness of solutions for the problem (1.1)–(1.2) with δ12 – 4δ0δ2 > 0 by applying Banach contraction mapping principle.

Results

Conclusion