SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Sobolev Type Nonlocal Fractional Stochastic Control Systems in Hilbert Spaces

A. Debbouche

Abstract
In this talk, we study a class of Sobolev type fractional control nonlocal functional differential equations in a Hilbert space. The results are obtained by using fractional calculus, semigroup theory, fixed point technique and optimal control. An appropriate set of sufficient conditions for the main results of the considered system is constructed and proved. As an application that illustrates the abstract results, provided examples are given.

Bibliography
[1] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
[2] Y. Zhou and F. Jiao, Existence of mild solutions for fractional neutral evolution equations, Computers and Mathematics with Applications 59, 1063-1077 (2010).
[3] P. J. Dauer and I. N. Mahmudov, Approximate controllability of semilinear functional equations in Hilbert spaces, J. Math. Anal. Appl. 273, 310-327 (2002).
[4] A. Debbouche and D. Baleanu, Controllability of Fractional Evolution Nonlocal Impulsive Quasilinear Delay Integro-Differential Systems, Computers and Mathematics with Applications 62, 1442-1450 (2011).

Organized by         Universidad de Valladolid     IMUVA