Hyers–Ulam stability for a class of Hadamard fractional Itô–Doob stochastic integral equations

Stability Results for a Class of Fractional Itô–Doob Stochastic Integral Equations

“…In stability concept, the Ulam stability was frst introduced by Ulam (see [10]) and then was generalized by Hyers and Rassias (see [11,12]). Many scientists generalized the Ulam-Hyers-Rassias results in various systems; for Hadamard fractional Itô-Doob stochastic integral equations and Caputo-derivative, we can refer to [13][14][15][16], and for fractional stochastic diferential equation with fractional Brownian motion and pantograph diferential equations, see [17][18][19][20][21].…”

“…One of the most important classes of fractional diferential equations are the fractional Itô-Doob stochastic diferential equations which had many applications in describing many phenomena of real life, and the nonlocal conditions describe numerous problems in physics (see [13,22,23]), fnance (see [24,25]), and mechanical problem (see [26,27]). To the best of our knowledge, there is no existing work on the Hyers-Ulam stability of fractional Itô-Doob stochastic integral equations.…”

Solvability of a Hadamard Fractional Boundary Value Problem at Resonance on Infinite Domain

“…In contrast to Riemann-Liouville and Caputo derivatives, Hadamard involves loga-rithmic function with arbitrary exponent. Many researchers have studied the Hadamard and Caputo-Hadamard fractional differential equations; for more details, see [7][8][9][10][11][12][13][14][15][16][17].…”

Fractional Itô–Doob Stochastic Differential Equations Driven by Countably Many Brownian Motions

“…One of the most famous class of the fractional equations are the fractional Itô-Doob stochastic differential equations (FIDSDEs). In the literature, there are a few papers on the FIDSDE (see [8][9][10][11]). In [9], the authors discuss the averaging principle of FIDSDE with NLC.…”