Almost automorphic solutions for fractional stochastic differential equations and its optimal control. (1st July 2015)

• Record Type: Journal Article
• Authors: Rajivganthi, C.; Muthukumar, P.
• Is Part Of: Optimal control applications and methods. Volume 37:Number 4(2016:Jul./Aug.)
• Page Start: 663
• Page End: 681
• Publication Date: 2015-07-01
• Subjects: fractional neutral stochastic differential equations -- Hilbert space -- optimal control -- Poisson jumps -- square‐mean almost automorphic solutions; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2186
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: Fractional calculus is the field of mathematical analysis that deals with the investigation and applications of integrals, derivatives of arbitrary order. The strength of derivatives of non‐integer order is their ability to describe real situations more adequately than integer order derivatives, especially when the problem has memory or hereditary properties. This paper is mainly concerned with the square‐mean almost automorphic mild solutions to a class of fractional neutral stochastic integro‐differential equations with infinite delay driven by Poisson jumps. The existence of square‐mean almost automorphic mild solutions of the previous fractional dynamical system is proved by using the method of successive approximation. The results are formulated and proved by using the fractional calculus, solution operator, and stochastic analysis techniques. Further, the existence of optimal control of the proposed problem is also presented. An example is provided to illustrate the developed theory. Copyright © 2015 John Wiley & Sons, Ltd.