Trajectory Controllability of Hilfer Fractional Neutral Stochastic Differential Equations with Deviated Argument Using Rosenblatt Process and Poisson Jumps

• Published in: Differential equations and dynamical systems Vol. 33; no. 2; pp. 453 - 474
• Main Authors: Chalishajar, D. N., Ramkumar, K., Ravikumar, K., Varshini, S.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Nature B.V 01.04.2025
• Subjects: Controllability; Differential equations; Dynamical systems; Fixed points (mathematics); Fractional calculus
• ISSN: 0971-3514; 0974-6870
• DOI: 10.1007/s12591-023-00632-3

The theoretical approach of Trajectory(T-)controllability of Hilfer fractional neutral stochastic differential equation with deviated arguments, Rosenblatt process and Poisson jumps has been elaborated. By knowing trajectories one can minimize the cost involved in the system. Our result extends the works of Chalishajar et al. (J Franklin Inst 347(7):1065–1075, 2010), Chalishajar et al. (Appl Math 3:1729–1738, 2012), Chalishajar et al. (Differential Equations and Dynamical Systems, Springer, Berlin, 2014) and the concept of Riemman-Liouville (R-L) and Caputo’s derivatives. A Hilfer Fractional Stochastic differential equation proposed here remains untreated in the literature and its solvability is acquired by using fractional calculus, stochastic analysis, semigroup theory and Krasnoselskii’s fixed point theorem. In the later part the T-controllability of the aforementioned system is calculated. An abstract phase space deinition has been used for the infinite delay T-control problem. Finally an illustration is given to validate our obtained results.