Title: Darboux problem for fractional order neutral functional partial hyperbolic differential equations

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, PR China

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 differential equations; neutral differential equations; hyperbolic differential equations; fractional order; solution; left-sided mixed Riemann–Liouville integral; Caputo fractional-order derivative; contraction; delay; fixed point theorem; initial value problems; Darboux problem.

DOI: 10.1504/IJDSDE.2009.031110

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.3/4, pp.301 - 312

Published online: 20 Jan 2010 *

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