Optimal Control Results for Sobolev-Type Fractional Stochastic Volterra-Fredholm Integrodifferential Systems of Order ϑ ∈ (1, 2) via Sectorial Operators
M. Johnson, V. Vijayakumar
Abstract
The objective of this paper is to investigate the optimal control results for Sobolev-type fractional stochastic Volterra-Fredholm integrodifferential systems of order ϑ∈(1,2) with sectorial operators in Hilbert spaces. Initially, we prove the existence of mild solutions by using fractional calculus, stochastic analysis theory, and the Schauder’s fixed point theorem. Next, we demonstrate the existence of optimal control pairs for the given system. Finally, an example is included to show the applications of the developed theory.
Topics & Concepts
MathematicsSobolev spaceFixed-point theoremType (biology)Order (exchange)Hilbert spaceFractional calculusApplied mathematicsOptimal controlMathematical analysisPure mathematicsMathematical optimizationEconomicsBiologyEcologyFinanceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsNumerical methods in engineering