What is it about?
The sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fBm via fixed point theorems.
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Why is it important?
This paper has advanced the controllability result of fractional order stochastic differential inclusions with fBm in finite dimensional space. The results have been obtained upon suitable fixed point theorems, namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler for the nonconvex case. Finally, a numerical example has been given to validate the efficiency of the proposed theoretical results.
Perspectives
Many real dynamical systems are better characterized by using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. The concept of fractional calculus has tremendous potential to change the model and control the nature around us. Fractional differential equations serve as an appropriate phenomenon such that it can even describe the real world problems which are impossible to describe using classical integer order differential equations. Over the past decades, the theory of fractional differential equation received more attention and has obtained a prior position in the field of physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electrochemistry and much other science and engineering areas.
P. Balasubramaniam
Gandhigram Rural Institute
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This page is a summary of: Controllability of fractional order stochastic differential inclusions with fractional Brownian motion in finite dimensional space, IEEE/CAA Journal of Automatica Sinica, October 2016, Institute of Electrical & Electronics Engineers (IEEE),
DOI: 10.1109/jas.2016.7510085.
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