Optimal controls for fractional stochastic differential systems driven by Rosenblatt process with impulses
Rajesh Dhayal, J. F. Gómez‐Aguilar, Guillermo Fernández‐Anaya
Abstract
Abstract The objective of this article is to consider a new class of fractional stochastic differential systems driven by the Rosenblatt process with impulses. We used fractional calculus, stochastic analysis, and Krasnoselskii's fixed point theorem to study the existence of piecewise continuous mild solutions for the proposed system. Further, we discussed the existence of optimal controls for the considered system. Our main results are well supported by an illustrative example.
Topics & Concepts
PiecewiseMathematicsFractional calculusApplied mathematicsClass (philosophy)Stochastic differential equationFixed-point theoremDifferential (mechanical device)Stochastic calculusPoint processStochastic processCalculus (dental)Mathematical optimizationDifferential equationMathematical analysisComputer scienceStochastic partial differential equationStatisticsDentistryAerospace engineeringArtificial intelligenceEngineeringMedicineNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsStability and Controllability of Differential Equations