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Báo cáo hóa học: " Research Article Global Uniqueness Results for Fractional Order Partial Hyperbolic Functional "

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Global Uniqueness Results for Fractional Order Partial Hyperbolic Functional | Hindawi Publishing Corporation Advances in Difference Equations Volume 2011 Article ID 379876 25 pages doi 10.1155 2011 379876 Research Article Global Uniqueness Results for Fractional Order Partial Hyperbolic Functional Differential Equations Said Abbas 1 Mouffak Benchohra 2 and Juan J. Nieto3 1 Laboratoire de Mathematiques Universite de Saida P.O. Box 138 Saida 20000 Algeria 2 Laboratoire de Mathematiques Universite de Sidi Bel-Abbes P.O. Box 89 Sidi Bel-Abbes 22000 Algeria 3 Departamento de Analisis Matemdtico Facultad de Matemdticas Universidad de Santiago de Compostela 15782 Santiago de Compostela Spain Correspondence should be addressed to Juan J. Nieto juanjose.nieto.roig@usc.es Received 22 November 2010 Accepted 29 January 2011 Academic Editor J. J. Trujillo Copyright 2011 Said Abbas etal. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. We investigate the global existence and uniqueness of solutions for some classes of partial hyperbolic differential equations involving the Caputo fractional derivative with finite and infinite delays. The existence results are obtained by applying some suitable fixed point theorems. 1. Introduction In this paper we provide sufficient conditions for the global existence and uniqueness of some classes of fractional order partial hyperbolic differential equations. As a first problem we discuss the global existence and uniqueness of solutions for an initial value problem IVP for short of a system of fractional order partial differential equations given by cDru x f x u if x e J f11 u x y x y u x x y e . 0 x y u x y fi x y if x y e J 1.2 u x 0 q x u 0 y V y x y e 0 to 1.3 where J 0 to X 0 to J -a to X -p to 0 to X 0 to a p 0 Ộ e C J R cD0 is the Caputo s fractional derivative of order r r1 r2 e 0 1 X 0 1 f J X C R is a given function Ự 0 to R V 0 to R are given .