A class of Hilfer fractional stochastic differential equations and optimal controls

Abstract

In this paper, we investigate a class of Hilfer fractional stochastic differential equations with nonlocal conditions. We first study the existence of mild solutions of these equations by means of stochastic analysis theory, fractional calculations, and operator semigroup theory. Further, the existence of optimal pairs for the corresponding Lagrange control systems is investigated. Finally, an example is presented to illustrate our obtained results.

Optimal Controls for Stochastic Functional Integrodifferential Equations M. A. Diop, P. D. A. Guindo, M. Fall, and A. Diakhaby

“…The optimal control theory has been successfully applied in biology, engineering, economy, physics, etc. (see [12]). In recent years, many efforts have been made to investigated the existence of optimal controls for various types of stochastic nonlinear functional differential equations in infinite dimensional spaces(see [21,25]).…”

Ulam–Hyers Stability for a Class of Hilfer-Type Fractional Stochastic Differential Equations

“…However, the systems of [23,24] are different. Lv and Yang [25] investigated the existence of HFSDEs by applying the fixed-point theorem and verified its uniqueness by using the contraction mapping principle.…”

Impulsive stochastic differential equations involving Hilfer fractional derivatives

“…For some fundamental results in the theory of differential equations involving Caputo and Riemann-Liouville fractional derivatives, please see [1,2,24,32,33,34,41] and the references therein. Since Hilfer [18] proposed the generalized Riemann-Liouville fractional derivative, there has been some interest in studying differential equations involving Hilfer fractional derivatives (see [10,11,20] and the references therein). Recently, considerable attention has been given to the existence of solutions of initial and boundary value problems for fractional differential equations with Hilfer fractional derivative [5,35,36].…”