Title: Fractional order partial hyperbolic functional differential equations with state-dependent delay

Authors: Said Abbas, Mouffak Benchohra, Yong Zhou

Addresses: Laboratoire de Mathematiques, Universite de Saida, B.P. 138, 20000, Saida, Algerie. ' Laboratoire de Mathematiques, Universite de Sidi Bel-Abbes, B.P. 89, 22000, Sidi Bel-Abbes, Algerie. ' Department of Mathematics, Xiangtan University, Hunan 411105, China

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 equations; solution; left-sided mixed Riemann-Liouville integral; Caputo fractional order derivative; state dependent delay; fixed point.

DOI: 10.1504/IJDSDE.2011.042941

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.4, pp.459 - 490

Published online: 24 Jan 2015 *

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