A variation of constant formula for Caputo-Hadamard fractional stochastic differential equations

This paper studies the existence and uniqueness of the mild solutions of Caputo-Hadamard fractional stochastic differential equations (SDEs). Subsequently, a variation of constants formula is derived for these equations. The primary proof techniques rely on It & ocirc;'s isometry, the martingale representation theorem, and the adaptation of the variation of constants formula employed in deterministic Caputo-Hadamard fractional differential equations (FDEs). Furthermore, we employ the constant variation formula to investigate the mean-square stability of a class of scalar Caputo-Hadamard fractional SDEs and provide stability criteria. Consequently, this class of scalar equations can serve as basic test equations to study the stability of numerical methods for Caputo-Hadamard fractional SDEs.