The least-squares linear inverse estimation problem for random fields is studied in a fractional generalized framework. First, the second-order regularity properties of the random fields involved in this problem are analysed in terms of the fractional Sobolev norms. Second, the incorporation of prior information in the form of a fractional stochastic model, with covariance operator bicontinuous...

We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi-Nash-Moser Hölder regularity theorem for solutions in a divergence form equation. We also prove results regarding existence, uniqueness, and higher regularity in time.

An inverse source problem for non-smooth multiterm time Caputo fractional diffusion with order designed as β0 < β1 ⋯ βM 1 is the case of study in a bounded Lipschitz domain $\mathbb {R}^{d}$ . The missing solely time-dependent function reconstructed from an additional integral measurement. existence, uniqueness and regularity weak solution investigated. We design numerical algorithm based on Ro...

We consider a half-order time-fractional diffusion equation in arbitrary dimension and investigate inverse problems of determining the source term or coefficient from spatial data at an arbitrarily fixed time under some additional assumptions. We establish stability estimate Lipschitz type proofs are based on Bukhgeim-Klibanov method by using Carleman estimates.

This paper is concerned with the numerical solutions of a variable-order space-time fractional reaction-diffusion model. The space-time fractional derivative is considered in the sense of Riesz-Feller, the system is defined by replacing the second order space derivatives with the variable Riesz-Feller derivatives. The problem is solved by an explicit finite difference method. Finally, simulatio...

As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly used in the related mathematical descriptions. These models usually involve long-time-range computation, which is a critical obstacle for their application; improvement of computational eff...