Existence of an optimal control for fractional stochastic partial neutral integro-differential equations with infinite delay

Yan, Zuomao¹ ; Lu, Fangxia²

¹ School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P. R. China
² Department of Mathematics,, Hexi University, Zhangye, Gansu 734000, P. R. China

Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 5, p. 557-577.

Résumé

In this paper we study optimal control problems governed by fractional stochastic partial neutral functional integro-differential equations with infinite delay in Hilbert spaces. We prove an existence result of mild solutions by using the fractional calculus, stochastic analysis theory, and fixed point theorems with the properties of analytic α-resolvent operators. Next, we derive the existence conditions of optimal pairs of these systems. Finally an example of a nonlinear fractional stochastic parabolic optimal control system is worked out in detail.

Détail

DOI : 10.22436/jnsa.008.05.10

Classification : 34G25, 34H05, 60H15, 26A33, 93E20
Keywords: Fractional stochastic partial neutral functional integro-differential equations, optimal controls, infinite delay, analytic α-resolvent operator, fixed point theorem.

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