Non-Instantaneous Impulsive Fractional Stochastic Differential Systems with Damping: Optimal Controls and Trajectory Controllability

Ravikumar Kasinathan, Varshini Sandrasekaran, Ramkumar Kasinathan and Rajesh Dhayal ()
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Ravikumar Kasinathan: PSG College of Arts & Science
Varshini Sandrasekaran: PSG College of Arts & Science
Ramkumar Kasinathan: PSG College of Arts & Science
Rajesh Dhayal: Thapar Institute of Engineering and Technology

Journal of Theoretical Probability, 2025, vol. 38, issue 3, 1-27

Abstract: Abstract We investigate a new class of impulsive fractional stochastic differential systems with damping effects in Banach spaces, where the abrupt changes occur suddenly at specific points and extend over finite time intervals. Initially, we explore the solvability of the system by applying stochastic analysis, fractional calculus, and the Banach contraction principle. Next, we utilize Balder’s theorem to establish the existence of optimal controls. Additionally, under certain conditions, we establish the trajectory controllability of the system by employing generalized Grönwall’s inequality. An example is provided to demonstrate the validity of the results.

Keywords: Existence; Optimal controls; Controllability; Fractional stochastic differential systems; Non-instantaneous impulses; 34K05; 34K30; 35B35; 93B05; 47H10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01423-y

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