The substantial, tempered, and shifted fractional derivatives, useful in medium range
systems, are reviewed and highlighted in a unified framework. Their historical evolution is …

In this paper, we develop a range of efficient and fast fractional difference schemes for the
approximation of Caputo time-fractional subdiffusion-reaction equations. The classical time …

In this paper, we study the following time-fractional Feynman-Kac equation-Δ G (x, t)= f (x,
t),~~~ 0< α< 1,~~ σ> 0. σ CD t α G (x, t)-Δ G (x, t)= f (x, t), 0< α< 1, σ> 0. As is well known, the …

In this paper, we constructed a linearized compact difference scheme for fourth order non-
linear fractional sub-diffusion equation with time delay and variable coefficients. The primary …

A novel second-order numerical approximation for the Riemann–Liouville tempered
fractional derivative, called the tempered fractional-compact difference formula is derived by …

Owing to the superior capability of fractional differential equations in modeling and
characterizing accurate dynamical properties of many high technology real world systems …

In the current paper, for the time fractional diffusion equation with an exponential tempering,
we propose a numerical algorithm based on the Lagrange-quadratic spline interpolations …

In this work, we present the correction schemes of the k-step BDF convolution quadrature at
the starting k-1 k-1 steps for the fractional Feynman–Kac equation with Lévy flight. Based on …

In this article, we consider high order discrete schemes for solving the time tempered
fractional diffusion equation. We present a semi-discrete scheme by using the local …

In this paper, we propose a compact difference scheme of second order temporal
convergence for the analysis of sub-diffusion fourth-order neutral fractional delay differential …