Electron. J. Diff. Equ., Vol. 2010(2010), No. 91, pp. 1-17.

Impulsive discontinuous hyperbolic partial differential equations of fractional order on Banach algebras

Said Abbas, Ravi P. Agarwal, Mouffak Benchohra

This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Caratheodory conditions and certain monotonicity conditions.

Submitted May 6, 2010. Published July 7, 2010.
Math Subject Classifications: 26A33.
Key Words: Impulsive differential equations; fractional order; upper solution; lower solution; extremal solutions; left-sided mixed Riemann-Liouville integral; Caputo fractional-order derivative; fixed point; Banach algebra.

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Saïd Abbas
Laboratoire de Mathématiques, Université de Saïda
B.P. 138, 20000, Saïda, Algérie
email: abbas_said_dz@yahoo.fr
Ravi P. Agarwal
Department of Mathematical Sciences
Florida Institute of Technology
Melboune, Florida, 32901-6975, USA
email: agarwal@fit.edu
Mouffak Benchohra
Laboratoire de Mathématiques, Université de Sidi Bel-Abbès
B.P. 89, 22000, Sidi Bel-Abbès, Algérie
email: benchohra@univ-sba.dz

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