The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm

Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods

“…There exists a unique linear transformation Δ : D 1 ⟶ D 2 such that the limit ΔðσÞ = lim n⟶+∞ hð2 n σÞ/2 n exists for each σ ∈ D 1 and khðσÞ − ΔðσÞk ≤ λ for all σ ∈ D 1 , which was the first step towards more answers in this area. Many researchers have analyzed the HUS of various classes of differential systems (see, for instance, [1,[6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). In 1978, Rassias [22] provided a generalized answer to the Ulam question for approximate λ-linear transformations.…”

“…In the literature, there are a few papers about the HUS and the HURS of stochastic systems (see [13,[27][28][29][30]). The stability of SFDEs has attracted much more attention (see [2,19] etc.).…”

Stabilization of Stochastic Differential Equations Driven by G-Brownian Motion with Aperiodically Intermittent Control

“…As we know, stability is one of the most interesting topics in dynamic behaviors. Regarding SDEs, many interesting works have been obtained on this issue (one can see [8,9]). Similarly, a lot of researchers have made great efforts on the subject of G-SDEs, for instance, exponential stabilization and quasi-sure exponential stabilization ( [10]).…”

Fourier Transformation and Stability of a Differential Equation on L 1

“…e result of the work of Alsina and Ger was extended to the Hyers-Ulam stability of a higher-order differential equation with constant coefficients in [6]. We mention here only the recent contributions in this subject of some mathematicians [6][7][8][9][10][11][12][13][14][15].…”