Over the past few decades, there has been substantial interest in evolution equations that
involve a fractional-order derivative of order α∈(0, 1) in time, commonly known as …

Fractional differential equations (FDES), ie, differential equations involving fractional-order
derivatives, have received much recent attention in engineering, physics, biology and …

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 …

We show global uniqueness in an inverse problem for the fractional Schrödinger equation:
an unknown potential in a bounded domain is uniquely determined by exterior …

Inverse problems of determining sources of the fractional partial differential equations Page
1 Yikan Liu, Zhiyuan Li, and Masahiro Yamamoto Inverse problems of determining sources …

The purpose of this book is to present a self-contained and up-to-date survey of numerical
treatment for the so-called time-fractional diffusion model and their mathematical analysis …

In this paper, we first establish a weak unique continuation property for time-fractional
diffusion-advection equations. The proof is mainly based on the Laplace transform and the …

The strong maximum principle is a remarkable property of parabolic equations, which is
expected to be partly inherited by fractional diffusion equations. Based on the corresponding …

Abstract Given (M, g), a compact connected Riemannian manifold of dimension d⩾ 2, with
boundary∂ M, we consider an initial boundary value problem for a fractional diffusion …

In the past several decades, in order to have quick and direct methods to perform production
forecasting and reserves estimation in practice, petroleum engineers have designed various …