Existence of solutions for several higher-order Hadamard-type fractional differential equations with integral boundary conditions on infinite interval

Wei Zhang,Wenbin Liu

doi:10.1186/s13661-018-1053-4

Abstract

In this paper, we investigate the existence of solutions for several higher-order integral boundary value problems of Hadamard-type fractional differential equations on an infinite interval by using the monotone iterative technique and Mawhin’s continuation theorem. The results enrich and extend some known conclusions of Hadamard-type fractional boundary value problems. Moreover, we give two concrete examples to illustrate the theoretical results.

Highlights

1 Introduction In recent years, the study of fractional differential equations (FDEs for short) has been an interesting and popular field of research as it plays an important role in many areas such as control theory, electrical circuits, biology, physics, diffusion processes, finance, etc
One of the interesting and important features of discussing FDEs is focused on the research of the existence solutions for nonlinear fractional initial value problems and fractional boundary value problems (BVPs for short)
5 Conclusion In this paper, by means of the monotone iterative technique and Mawhin’s continuation theorem, we have proved the existence of solutions for two types of higher-order Hadamard-type FDEs with integral boundary conditions on an infinite interval

Summary

Introduction

The study of fractional differential equations (FDEs for short) has been an interesting and popular field of research as it plays an important role in many areas such as control theory, electrical circuits, biology, physics, diffusion processes, finance, etc. (see [1,2,3,4,5,6,7,8]). We study the existence of solutions for the following Hadamard-type Lemma 3.3 (see [25]) Let V = {x ∈ E : x E ≤ r, r > 0} ⊂ E be relatively compact in E if the following conditions hold: (i)

Results

Conclusion