Controllability of fractional neutral stochastic functional differential systems

In this paper, we study a class of fractional neutral stochastic functional differential systems. We obtain the controllability of the stochastic functional differential systems by the Sadovskii’s fixed point theorem under some suitable assumptions. An example is given to illustrate the theory.

[1]  I. Podlubny Fractional differential equations , 1998 .

[2]  Pagavathigounder Balasubramaniam,et al.  Approximate Controllability of Neutral Stochastic Functional Differential Systems with Infinite Delay , 2010 .

[3]  Marjorie G. Hahn,et al.  Fokker-Planck-Kolmogorov equations associated with time-changed fractional Brownian motion , 2010, 1002.1494.

[4]  Pagavathigounder Balasubramaniam,et al.  Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space , 2006 .

[5]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .

[6]  J. Craggs Applied Mathematical Sciences , 1973 .

[7]  Rathinasamy Sakthivel,et al.  Approximate controllability of fractional stochastic evolution equations , 2012, Comput. Math. Appl..

[8]  Hamdy M. Ahmed,et al.  Controllability of fractional stochastic delay equations , 2009 .

[9]  L. P. Kok,et al.  Table errata: Higher transcendental functions, Vol. III [McGraw-Hill, New York, 1955; MR 16, 586] by A. Erdélyi, W. Magnus, F. Oberhettinger and F. G. Tricomi , 1983 .

[10]  S L Wearne,et al.  Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Zuomao Yan,et al.  Controllability of fractional-order partial neutral functional integrodifferential inclusions with infinite delay , 2011, J. Frankl. Inst..

[12]  F. Viens,et al.  Stochastic evolution equations with fractional Brownian motion , 2003 .

[13]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[15]  Emilia Bazhlekova,et al.  Fractional evolution equations in Banach spaces , 2001 .

[16]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[17]  Yong Zhou,et al.  Existence and controllability results for fractional semilinear differential inclusions , 2011 .

[18]  Nazim I. Mahmudov,et al.  Controllability of semilinear stochastic systems in Hilbert spaces , 2003 .

[19]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

[20]  B. N. Sadovskii A fixed-point principle , 1967 .

[21]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .

[22]  F. Mainardi Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models , 2010 .

[23]  Jinghuai Gao,et al.  Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness , 2012 .

[24]  Yong Zhou,et al.  Existence of mild solutions for fractional neutral evolution equations , 2010, Comput. Math. Appl..

[25]  Rathinasamy Sakthivel,et al.  Controllability for a class of fractional-order neutral evolution control systems , 2012, Appl. Math. Comput..

[26]  Litan Yan,et al.  Existence result for fractional neutral stochastic integro-differential equations with infinite delay , 2011 .

[27]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[28]  Nazim I. Mahmudov,et al.  Controllability of stochastic semilinear functional differential equations in Hilbert spaces , 2004 .

[29]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .