Electron. J. Diff. Equ., Vol. 2012 (2012), No. 103, pp. 1-9.

Existence and uniqueness of solutions to functional integro-differential fractional equations

Moulay Rchid Sidi Ammi, El Hassan El Kinani, Delfim F. M. Torres

Using a fixed point theorem in a Banach algebra, we prove an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result are also obtained.

Submitted January 27, 2012. Published June 20, 2012.
Math Subject Classifications: 26A33, 47H10.
Key Words: Riemann-Liouville operator; fractional calculus; fixed point theorem; Lipschitz condition.

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Moulay Rchid Sidi Ammi
Faculty of Sciences and Techniques
Moulay Ismail University, AMNEA Group
Errachidia, Morocco
email: sidiammi@ua.pt
El Hassan El Kinani
Faculty of Sciences and Techniques
Moulay Ismail University, GAA Group
Errachidia, Morocco
email: elkinani_67@yahoo.com
Delfim F. M. Torres
Center for Research and Development in Math. and Appl. (CIDMA)
Department of Mathematics, University of Aveiro
Campus Universitário de Santiago
3810-193 Aveiro, Portugal
email: delfim@ua.pt

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