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Almost automorphic solutions for fractional stochastic differential equations and its optimal control

机译：分数阶随机微分方程的概亚纯解及其最优控制

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摘要

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 (c) 2015 John Wiley & Sons, Ltd.
机译：分数演算是数学分析领域，致力于研究和应用积分，任意阶导数。非整数阶导数的优势在于，它们比整数阶导数更能充分描述实际情况的能力，尤其是当问题具有记忆或遗传特性时。本文主要关注由泊松跳跃驱动的具有无限时滞的分数阶中立型随机积分-微分方程的平方均值几乎自同构温和解。利用逐次逼近的方法证明了分数阶动力系统平方均值几乎自同构温和解的存在性。通过使用分数演算，求解算子和随机分析技术来制定和证明结果。此外，还提出了对所提出问题的最优控制的存在。提供了一个例子来说明已发展的理论。版权所有（c）2015 John Wiley＆Sons，Ltd.

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