Semigroup-based theoretical prospects on optimal control of stochastic second-order Gurtin–Pipkin integro-differential equations

作者：K. Anukiruthika, P. Muthukumar, Pratibhamoy Das · 发表于：Optimization · 年份：2025 · DOI：10.1080/02331934.2025.2534119 · 被引用次数：28

The present study demonstrates the solvability and the existence of optimal control for the second-order hyperbolic Gurtin–Pipkin-type stochastic integro-differential equations involving mixed fractional Brownian motions. To generalize the existing deterministic Gurtin–Pipkin-type equation, the memory effect and disturbances are modelled using stochastic perturbations. This work addresses solvability through stochastic analysis, semigroup theory and fixed-point approach. Also, the continuous dependence of solutions on the initial condition; is proved. The existence of optimal control is provided using the Balder's theorem. To justify the importance of the proposed study, an example is illustrated at the end.