J. Nonl. Evol. Equ. Appl. 2014 (1), pp. 1-12, published on August 25, 2014:

Ulam Stability for Impulsive Discontinuous Partial Fractional Differential Equations in Banach Algebras

S. Abbas

Laboratory of Mathematics, University of Saïda, PO Box 138, 20000 Saïda, Algeria

M. Benchohra

Laboratory of Mathematics, University of Sidi Bel-Abbès, P.O. Box 89, 22000, Sidi Bel-Abbès, Algeria
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received on September 6, 2013
Accepted on January 17, 2014

Communicated by Gisèle Mophou

Abstract.  In this paper, we investigate some existence and Ulam’s type stability concepts of fixedpoint inclusions for a class of partial discontinuous fractional order differential equations with impulses in Banach algebras.
Keywords: Partial fractional differential equation, left-sided mixed Riemann–Liouville integral, Caputo fractional-order derivative, fixed point equation, Banach algebra, impulse, Ulam–Hyers stability.
2010 Mathematics Subject Classification:   26A33, 34G20, 34A40, 45N05, 47H10.

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