Positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions

Jiqiang Jiang,Jiafa Xu,Zhengqing Fu,Donal O’Regan

doi:10.1186/s13660-019-2156-x

Abstract

In this paper we use the fixed point index to study the existence of positive solutions for a system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions. Here we use appropriate nonnegative matrices to depict the coupling behavior for our nonlinearities.

Highlights

1 Introduction In this paper we consider the system of nonlinear Hadamard fractional differential equations involving coupled integral boundary conditions
In this paper we study the existence of positive solutions for the system of nonlinear Hadamard fractional differential equations (1.1) involving coupled integral boundary conditions
= 0, uniformly on t ∈ [1, e], a21x+b21y→0+ a21x + b21y 3x+3y→0+ 3x + 3y and lim sup (600x + 7y)γ2

Summary

Introduction

Fractional-order differential equations is a rapidly developing area of research; we refer the reader to [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48] and the references therein. In [1] the authors studied positive solutions for the p-Laplacian fractional Riemann–

Stieltjes integral boundary value problem

This proves that