Asymptotic separation between solutions of Caputo fractional stochastic differential equations

On the Construction of Some Fractional Stochastic Gompertz Models

“…Since y ν 1 (t) = αΨ ν 1 (t), we have shown that y ν 1 (t) = r ν 1 (t) and we achieve Equation (25). Thus, we can conclude that equation…”

“…In Section 4 we give some examples on possible choices of noise. In particular in Section 4.4 we show that such fractional-integral equations are indeed a generalization of the fractional stochastic differential equations discussed in [24,25].…”

“…To do this, we first need to investigate some results related to a class of stochastic linear fractional-integral equations, concerning in particular the existence of Gaussian solutions. Such equations generalize the Caputo-fractional stochastic differential equations studied for instance in [24,25].…”

“…where W is a Brownian motion on (Ω, F , F t , P) and the integral must be interpreted in the Itô sense. With this noise, Equation (12) is the integral version of a Caputo-fractional stochastic differential equation, as studied for instance in [24,25]. For such equations, closed form of the solutions can be obtained via a variation of constant formula, as shown in [24].…”

On the asymptotic behavior of solutions to time-fractional elliptic equations driven by a multiplicative white noise

“…is said to be F-adapted if ξ(t) ∈ X t for all t ≥ 0. We now restate the notion of classical solution to 1, see e.g., [2, p. 209] and [20].…”