Systems of generalized Sturm-Liouville and Langevin fractional differential equations

Thanadon Muensawat,Sotiris K Ntouyas,Jessada Tariboon

doi:10.1186/s13662-017-1114-5

Abstract

In this paper, we study anti-periodic boundary value problems for systems of generalized Sturm-Liouville and Langevin fractional differential equations. Existence and uniqueness results are proved via fixed point theorems. Examples illustrating the obtained results are also presented.

Highlights

1 Introduction Fractional differential equations have attracted the attention of many researchers working in a variety of disciplines due to the development and applications of these equations in many fields such as engineering, mathematics, physics, chemistry, etc
The study of boundary value problems of coupled systems of fractional order differential equations is very important as such systems appear in a variety of problems of applied nature, especially in biosciences, for instance, see [ – ]
In [ ], the authors proposed an approach to the fractional version of the Sturm-Liouville problem. They investigated the eigenvalues and eigenfunctions associated with these operators and their properties with the objective of applying this generalized Sturm-Liouville theory to fractional partial differential equations

Summary

Introduction

Fractional differential equations have attracted the attention of many researchers working in a variety of disciplines due to the development and applications of these equations in many fields such as engineering, mathematics, physics, chemistry, etc. The classical Sturm-Liouville problem for a linear differential equation of second order is a boundary-value problem as the following one: They investigated the eigenvalues and eigenfunctions associated with these operators and their properties with the objective of applying this generalized Sturm-Liouville theory to fractional partial differential equations.

Results

Conclusion