Int. J. Dynamical Systems and Differential Equations, Vol. 3, No. 4, 2011 459
Fractional order partial hyperbolic functional
differential equations with state-dependent delay
Saïd Abbas
Laboratoire de Mathématiques,
Université de Saïda,
B.P. 138, 20000, Saïda, Algérie
E-mail: abbasmsaid@yahoo.fr
Mouffak Benchohra
Laboratoire de Mathématiques,
Université de Sidi Bel-Abbès,
B.P. 89, 22000, Sidi Bel-Abbès, Algérie
E-mail: benchohra@univ-sba.dz
Yong Zhou*
Department of Mathematics,
Xiangtan University,
Hunan 411105, China
E-mail: yzhou@xtu.edu.cn
*Corresponding author
Abstract: This paper deals with the existence and uniqueness of solutions
of some classes of partial functional and neutral functional hyperbolic
differential equations with state-dependent delay involving the Caputo
fractional derivative. Our results will be obtained by using suitable fixed
point theorems.
Keywords: partial differential equation; fractional order; solution;
left-sided mixed Riemann-Liouville integral; Caputo fractional-order
derivative; state-dependent delay; fixed point.
Reference to this paper should be made as follows: Abbas, S.,
Benchohra, M. and Zhou, Y. (2011) ‘Fractional order partial
hyperbolic functional differential equations with state-dependent delay’,
Int. J. Dynamical Systems and Differential Equations, Vol. 3, No. 4,
pp.459–490.
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.
Mouffak Benchohra is a Professor of Mathematics at the University
of Sidi Bel Abbes, Algeria. His research interests include fractional
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