Ulam–Hyers–Rassias stability of Hilfer fractional stochastic impulsive differential equations with non-local condition via Time-changed Brownian motion followed by the currency options pricing model

Abstract

In this paper, a new solution representation and Ulam-Hyer’s Rassias stability of Hilfer fractional stochastic impulsive differential systems (HFSIDEs) with non-local condition via Time-changed fractional Brownian motion (TCFBM) is studied. The wellposedness of solutions are proved in the finite-dimensional space by using fixed point theorem (FPT). Finally, to account for the long-memory property of the spot exchange rate, we offer a novel framework for pricing currency options in line with the TCFBM model.