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. | |