Optimal Control Results for Sobolev-Type Fractional Stochastic Volterra-Fredholm Integrodifferential Systems of Order ϑ ∈ (1, 2) via Sectorial Operators

Abstract

The objective of this paper is to investigate the optimal control results for Sobolev-type fractional stochastic Volterra-Fredholm integrodifferential systems of order $\vartheta \in (1,2)$ 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.

Keywords:

• Fractional calculus
• mild solution
• optimal controls
• Sobolev-type system
• stochastic integrodifferential systems

2010 SUBJECT CLASSIFICATION:

• 34A08
• 34K35
• 45D05
• 58C30
• 60H10