The Mittag-Leffler (ML) function plays a fundamental role in fractional calculus but very few
methods are available for its numerical evaluation. In this work we present a method for the …

In this paper, a linearized L1-Galerkin finite element method is proposed to solve the
multidimensional nonlinear time-fractional Schrödinger equation. In terms of a temporal …

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some
applications in fractional calculus, are discussed. In general the evaluation of a scalar …

We study a fully discretized finite element approximation to variable-order Caputo and
Riemann–Liouville time-fractional diffusion equations (tFDEs) in multiple space dimensions …

This paper obtains analytical solution of nonlinear Schrödinger equation in both time and
space fractional terms. Two analytical approaches, Nucci's reduction method and simplest …

A class of high-order numerical algorithms for Riesz derivatives are established through
constructing new generating functions. Such new high-order formulas can be regarded as …

Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in a second order
in time partial integro-differential equation. In this paper, we consider a nonlinear model of …

一类非线性时间分数阶扩散方程反问题的变分型正则化* Page 1 应用数学和力学编委会,ISSN
1000-0887 http://www.applmathmech.cn 一类非线性时间分数阶扩散方程 反问题的变分型正则化 …

The space-time fractional nonlinear Schrödinger equation is solved by mean of on the
fractional Riccati expansion method. These solutions include generalized trigonometric and …

This paper is concerned with design and analysis of a high order numerical approach based
on a uniform mesh to approximate the solution of time-fractional fourth order partial …