Hilfer fractional neutral stochastic differential equations with non-instantaneous impulses

Convergence on iterative learning control of Hilfer fractional impulsive evolution equations

“…As stochastic differential equations have many applications in the field of science and technology, the study of ILC for non-instantaneous stochastic systems with Hilfer fractional derivative will be an interesting case to discuss. Recent articles on Hilfer fractional stochastic systems by Kasinathan et al [29] and article by Saravanakumar and Balasubramaniam [30] can be referred for details. Also, this theory can be developed for discrete system and can be studied further for delay systems.…”

Impulsive stochastic differential equations involving Hilfer fractional derivatives

“…Ahmed and El-Borai [4] investigated the existence of mild solutions of Hilfer fractional stochastic integro-differential equations with nonlocal conditions. Kasinathan et al [22] investigated the existence of mild solution of Hilfer fractional neutral stochastic differential equations with non-instantaneous impluses.…”

Ulam–Hyers Stability for a Class of Hilfer-Type Fractional Stochastic Differential Equations

“…[23] proved the existence of solutions to HFSDEs with noninstantaneous impulsive by utilizing the Mönch fixed-point theorem. In [24], the authors used the same method to study HFSDEs. However, the systems of [23,24] are different.…”

“…In [24], the authors used the same method to study HFSDEs. However, the systems of [23,24] are different. Lv and Yang [25] investigated the existence of HFSDEs by applying the fixed-point theorem and verified its uniqueness by using the contraction mapping principle.…”