Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space |
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| Authors: | Sathiyaraj T Balasubramaniam P |
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| Affiliation: | Department of Mathematics, The Gandhigram Rural Institute-Deemed University, Gandhigram-624302, Dindigul, Tamil Nadu, India |
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| Abstract: | In this paper, sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion (fBm) via fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case. The controllability Grammian matrix is defined by using Mittag-Leffler matrix function. Finally, a numerical example is presented to illustrate the efficiency of the obtained theoretical results. |
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| Keywords: | Controllability fractional Brownian motion fractional order derivatives Mittag-Leffler function stochastic differential inclusions |
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