J. Nonl. Evol. Equ. Appl. 2012 (7), pp. 85-96, published on December 1, 2012:

Asymptotic Stability in Nonlinear Delay Differential Equations of Fractional Order

S. Abbas

Laboratoire de Mathématiques, Université de Saïda, B.P. 138, 20000, Saïda, Algérie

M. Benchohra

Laboratoire de Mathématiques, Université de Sidi Bel-Abbès; B.P. 89, 22000, Sidi Bel-Abbès, Algérie

G. N’Guérékata

Department of Mathematics, Morgan State University; 1700 E. Cold Spring Lane, Baltimore M.D. 21252, USA

Received on March 12, 2012
Accepted on June 18, 2012 (with modifications)

Communicated by Claudio Cuevas

Abstract.  Our aim in this work is to study the existence and the local stability of solutions for a system of nonlinear delay partial differential equations of fractional order. We use the Schauder fixed point theorem for the existence of solutions, and we prove that all solutions are locally asymptotically stable.
Keywords: Delay differential equation; left-sided mixed Riemann-Liouville integral of fractional order; Caputo fractional-order derivative; stability; solution; fixed point.
2010 Mathematics Subject Classification:   26A33, 34A08, 34K20, 34K37.

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