A generalized quasi-reversibility regularization method for reconstructing source terms in a time-fractional fourth-order diffusion equation driven by fractional Brownian motion

Fourier Regularization for a Time-Fractional Source Problem

We study the inverse problem of identifying an unknown time-dependent source in a linear time-fractional diffusion equation, where the time derivative is taken in the Caputo sense of fractional order α . The problem is ill-posed in the sense of Hadamard: the solution does not depend continuously on the measured data, s...

Simultaneous Recovery of Space-Dependent Sources and Fractional Orders in Nonlocal Diffusion Equations from Final Data

Recovering the Fractional Order and an Initial Value Simultaneously in a Time-Fractional Diffusion-Wave Equation

For a one-dimensional time-fractional diffusion-wave equation, we investigate joint recovery of its fractional order and the initial velocity from measurements taken at one interior point. Uniqueness is proved through analytic continuation, Laplace transforms, an integral mean value theorem, and Mittag-Leffler function...

Space-time fractional stochastic Burgers-type equation

We establish the existence and uniqueness of solutions to a $(1+1)$-dimensional fractional stochastic Burgers-type equation featuring a Caputo fractional time derivative, a fractional Laplacian, and space-time white noise forcing modified by a Riemann-Liouville fractional integral. From a physical perspective, equation...

A coercive space-time variational approach to fractional diffusion problems

We consider a fractional diffusion problem with temporal nonlocality acting on the diffusive flux. A coercive space--time variational formulation in Bochner-valued fractional Sobolev spaces is derived and the existence, uniqueness, and regularity of solutions are established. We further develop a conforming tensor-prod...

Monte Carlo Approximations of Time-Nonlocal Diffusions in Bounded Domains

We develop and analyze a Monte Carlo method for sampling killed anomalous diffusions obtained by time-changing Brownian motion with drift by the inverse of a subordinator. The method targets probabilistic representations of time-nonlocal, including time-fractional, Cauchy--Dirichlet problems on bounded domains. Since i...