Int. J. Dynamical Systems and Differential Equations, Vol. 2, Nos. 3/4, 2009 301 Darboux problem for fractional order neutral functional partial hyperbolic differential equations Saïd Abbas Laboratoire de Mathématiques, Université de Saïda, B.P. 138, 20000, Saïda, Algérie E-mail: abbas_said_dz@yahoo.fr Mouffak Benchohra* Laboratoire de Mathématiques, Université de Sidi Bel-Abbès, B.P. 89, 22000, Sidi Bel-Abbès, Algérie E-mail: benchohra@yahoo.com E-mail: benchohra@univ-sba.dz *Corresponding author Yong Zhou Department of Mathematics, Xiangtan University, Hunan 411105, PR China E-mail: yzhou@xtu.edu.cn Abstract: In this paper, we prove an existence result for initial value problems (IVP for short), for neutral partial hyperbolic differential equations with finite delay involving the Caputo fractional derivative. Our works will be considered by using Krasnoselskii’s fixed point theorem. Keywords: functional hyperbolic neutral differential equations; fractional order; solution; left-sided mixed Riemann–Liouville integral; Caputo fractional-order derivative; contraction; delay; fixed point. Reference to this paper should be made as follows: Abbas, S., Benchohra, M. and Zhou, Y. (2009) ‘Darboux problem for fractional order neutral functional partial hyperbolic differential equations’, Int. J. Dynamical Systems and Differential Equations, Vol. 2, Nos. 3/4, pp.301–312. Biographical notes: Saïd Abbas is a Lecturer at the University of Saida. He received his Master Thesis from the University of Mostaganem. His research interests include fractional order partial hyperbolic differential equations. Copyright © 2009 Inderscience Enterprises Ltd.