Controllability of fractional stochastic neutral integro-differential equations with state-dependent delay in Frechet spaces

R, Pradeepa; R, Jayaraman

doi:10.30511/ttmp.2025.2043936.1043

Controllability of fractional stochastic neutral integro-differential equations with state-dependent delay in Frechet spaces

Document Type : Original Article

Authors

Pradeepa R ¹

Jayaraman R ²

¹ Paavai Engineering College

² Department of Mathematics, Government Arts and Science College, Pappireddipatti, Tamil Nadu, India.

10.30511/ttmp.2025.2043936.1043

Abstract

This paper explores the existence and controlla-
bility of state-dependent delay functionally neutral stochas-
tic fractional integro-differential equations within Frechet
spaces. By employing fixed point techniques, solution oper-
ator characteristics, and fractional calculus, we have estab-
lished the conditions for these systems’ controllability. The
findings are significant in extending the theoretical frame-
work of fractional differential equations with practical im-
plications in various scientific fields. An illustrative exam-
ple is provided to demonstrate the application of the main
results. This research contributes to the deeper understand-
ing and potential application of fractional stochastic systems
in diverse disciplines.

Keywords

Fractional differential equations

solution operator

stochastic differential system

state-dependent delay and fixed point theorem

Subjects