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

Recently, fractional differential equations have attracted great attention and many studies
have been performed. However, there are not many works that cover the theory of partial …

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 work, we consider a time-fractional Allen–Cahn equation, where the conventional first
order time derivative is replaced by a Caputo fractional derivative with order α ∈ (0, 1) …

Time-fractional initial-boundary value problems of the form are considered, where is a
Caputo fractional derivative of order and the spatial domain lies in for some. As we prove …

Variable-order space-time fractional diffusion equations, in which the variation of the
fractional orders determined by the fractal dimension of the media via the Hurst index …

A survey is given of convergence results that have been proved when the L1 scheme is
used to approximate the Caputo time derivative Dα t (where 0< α< 1) in initial-boundary …

A time-step** L1 scheme for subdiffusion equation with a Riemann--Liouville time
fractional derivative is developed and analyzed. This is the first paper to show that the L1 …

Accurate solutions of nonlinear multi-dimensional delay problems of fractional-order arising
in mathematical physics and engineering recently have been found to be a challenging task …

This paper is concerned with long time numerical behaviors of nonlinear fractional
pantograph equations. The L1 method with the linear interpolation procedure is applied to …