Over the last two decades, anomalous diffusion processes in which the mean squares
variance grows slower or faster than that in a Gaussian process have found many …

Physics-informed neural networks (PINNs), introduced in M. Raissi, P. Perdikaris, and G.
Karniadakis, J. Comput. Phys., 378 (2019), pp. 686--707, are effective in solving integer …

The subdiffusion equation with a Caputo fractional derivative of order in time arises in a wide
variety of practical applications, and it is often adopted to model anomalous subdiffusion …

We consider the initial/boundary value problem for a diffusion equation involving multiple
time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space …

We consider initial/boundary value problems for the subdiffusion and diffusion-wave
equations involving a Caputo fractional derivative in time. We develop two fully discrete …

This paper deals with an inverse problem of simultaneously identifying the space-dependent
diffusion coefficient and the fractional order in the 1D time-fractional diffusion equation with …

In this paper, we consider an inverse source problem for a time-fractional diffusion equation
with variable coefficients in a general bounded domain. That is to determine a space …

We consider the initial-boundary value problem for an inhomogeneous time-fractional
diffusion equation with a homogeneous Dirichlet boundary condition, a vanishing initial data …

In this paper, an inverse problem of determining a time-dependent source term in a one-
dimensional time-fractional diffusion equation from the energy measurement is studied. This …

We consider a linear heat equation involving a fractional derivative in time, with a nonlocal
boundary condition. We determine a source term independent of the space variable, and the …