Related papers: An inverse random source problem for the time frac…

In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…

In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reactiondiffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then…

We consider an inverse source problem in the two-time-scale mobile-immobile fractional diffusion model from partial interior observation. Theoretically, we combine the fractional Duhamel's principle with the weak vanishing property to…

In this paper, we investigate the inverse problem of determining the right-hand side of a subdiffusion equation with a Caputo time derivative, where the right-hand side depends on both time and certain spatial variables. Similar inverse…

In the present work, we discuss a unique solvability of an inverse-source problem with integral transmitting condition for time-fractional mixed type equation in a rectangular domain, where the unknown source term depends on space variable…

In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the…

In this paper, we investigate direct and inverse source problems for the diffusion equation with two-term generalized fractional derivative (Hilfer derivative) in a rectangular domain. Using spectral expansion method, we derive two-term…

In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville…

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2<H<1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its…

Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…

In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time-changed by an inverse stable subordinator whose index equals the order of…

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson…

Reaction-diffusion equations are one of the most common partial differential equations used to model physical phenomenon. They arise as the combination of two physical processes: a driving force $f(u)$ that depends on the state variable $u$…

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…

We deal with complex spatial diffusion equations with time-fractional derivative and study their stochastic solutions. In particular, we complexify the integral operator solution to the heat-type equation where the time derivative is…

This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…

This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…

This paper is concerned with the direct and inverse random source scattering problems for elastic waves where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the…