Semilinear functional differential equations with fractional order and finite delay

Mohammed Belmekkia, Kheira Mekhalfib and Sotiris K. Ntouyasc,*

Semilinear functional differential equations with fractional order and finite delay

Authors :

Mohammed Belmekki^a, Kheira Mekhalfi^b and Sotiris K. Ntouyas^c,*

Author Address :

^a,bDepartment of Mathematics, Saida University, BP 138, 20000 Saida, Algeria.

^cDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, Greece.

*Corresponding author.

Abstract :

In this paper, we establish sufficient conditions for existence and uniqueness of solutions for semilinear functional differential equations with finite delay involving the Riemann-Liouville fractional derivative. Our approach is based on resolvent operators, the Banach contraction principle, and the nonlinear alternative of Leray-Schauder type.

Keywords :

Semilinear functional differential equation, fractional derivative, fractional integral, fixed point, mild solutions, resolvent operator.

DOI :

Article Info :

Received : September 12, 2012; Accepted : October 27, 2012.