New existence and uniqueness results for an  $\alpha$ order boundary value problem

Zoubir Dahmania,* and Mohamed Amin Abdellaouib

New existence and uniqueness results for an $\alpha$ order boundary value problem

Authors :

Zoubir Dahmani^a,*and Mohamed Amin Abdellaoui^b

Author Address :

^a,bLaboratory of Pure and Applied Mathematics, LPAM, Faculty SEI, UMAB University of Mostaganem, Algeria.

*Corresponding author.

Abstract :

This paper is concerned with the existence of solutions for a non local fractional boundary value problem with integral conditions. New existence and uniqueness results are established using Banach fixed point theorem. Other existence results are obtained using Schauder and Krasnoselskii theorems. As an application, we give an example to illustrate our results.

Keywords :

Caputo derivative, fixed point theorem, boundary value problem.

DOI :

Article Info :

Received : January 21, 2013; Accepted : July 10, 2013.