Stochastic pseudo-parabolic equations with fractional derivative and fractional Brownian motion

Identifying inverse source for diffusion equation with conformable time derivative by Fractional Tikhonov method

“…Due to singular value decomposition for compact self-adjoint operator K, as in (13). If the measured data ℓ ϵ and ℓ with a noise level of ϵ satisfy∥ℓ − ℓ ϵ ∥ L 2 (Ω) ≤ ϵ then we can present a regularized solution as follows:…”

“…. (see [7][8][9][10][11][12][13][14][15] and references therein). Each defines fractional derivatives with properties that are advantageous in certain applications.…”

Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative

“…The direct problems for the time-fractional diffusion equation have been studied for many years, for example, the maximum principle, uniqueness results, existence results, numerical solutions, and analytic solutions [9][10][11][12][13][14][15][16][17]. In addition, various inverse problems of fractional diffusion equations have been researched extensively, such as inverse source problems [18,19], backward problems [20,21], the Cauchy problem [22,23], the inversion for parameter, or fractional order [24][25][26][27][28][29].…”

New results for stochastic fractional pseudo-parabolic equations with delays driven by fractional Brownian motion

“…In the deterministic case, some studies have been reported to fractional pseudo-parabolic equation, for example Sousa and Oliveira [49], Tuan et al [53], Tuan and Caraballo [54]. Fractional stochastic pseudo-parabolic equations driven by fractional Brownian motion were probably first studied by Thach and Tuan [52]. Indeed, they established the existence, uniqueness, regularity results for mild solutions to an initial value problem for considered equations in two cases of H, i.e, H > 1/2 and H < 1/2.…”