Existence and uniqueness of solution for a boundary value problem of fractional order involving two Caputo’s fractional derivatives

Mohamed I Abbas

doi:10.1186/s13662-015-0581-9

Abstract

In this paper we prove the existence and uniqueness of solution for a boundary value problem of fractional order involving two Caputo’s fractional derivatives. Our investigation is based on Holder’s inequality together with Banach contraction principle and Schaefer’s fixed point theorem.

Highlights

1 Introduction Boundary value problems for fractional differential equations arise from the study of models of viscoelasticity, electrochemistry, control, porous media, electromagnetic, etc
The attention drawn to the theory of the existence, multiplicity, and uniqueness of solutions to boundary value problems for fractional order differential equations is evident from the increased number of recent publications; see, for example, [, ] and [ ], and the references therein
Motivated by the above work, we investigate the existence and uniqueness of solution for a boundary value problem of fractional differential equation of the form

Summary

Introduction

Boundary value problems for fractional differential equations arise from the study of models of viscoelasticity, electrochemistry, control, porous media, electromagnetic, etc. (see [ , ] and [ ]). Quite recently, the theory of boundary value problems for fractional differential equations has received attention from many researchers. The attention drawn to the theory of the existence, multiplicity, and uniqueness of solutions to boundary value problems for fractional order differential equations is evident from the increased number of recent publications; see, for example, [ , ] and [ ], and the references therein.

Results

Conclusion