An existence and uniqueness theorem for fuzzy H-integral equations of fractional order

Mouffak Benchohraa,b,* and Abderrahmane Boukenkoulc

An existence and uniqueness theorem for fuzzy H-integral equations of fractional order

Authors :

Mouffak Benchohra^a,b,* and Abderrahmane Boukenkoul^c

Author Address :

^aLaboratory of Mathematics, University of Sidi Bel Abbes, Algeria, PO Box 89 Sidi Bel Abbes 22000, Algeria.

^bDepartment of Mathematics, King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia.

^cDepartement de Foresterie et d’Agronomie, Faculte des sciences de la vie et de l’environnement, Universite Abou Bekr Belkaid, Tlemcen, Algerie.

*Corresponding author.

Abstract :

We present an existence and uniqueness theorem for H- integral equations of fractional order involving fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi
continuous and compactly supported fuzzy sets in $mathbb{R}^n$. The method of successive approximation is the main tool in our analysis.

Keywords :

Fuzzy mapping, fractional orders, Riemann-Liouville H-differentiability, Fuzzy H-integral equation, Hausdorff metric, successive approximation.

DOI :

Article Info :

Received : November 20, 2013; Accepted : February 16, 2014.