It is well known that the trapezoidal rule converges geometrically when applied to analytic
functions on periodic intervals or the real line. The mathematics and history of this …

Fractional differential equations are becoming increasingly used as a powerful modelling
approach for understanding the many aspects of nonlocality and spatial heterogeneity …

The purpose of this work is to study solution techniques for problems involving fractional
powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary …

Impulse propagation in biological tissues is known to be modulated by structural
heterogeneity. In cardiac muscle, improved understanding on how this heterogeneity …

The paper describes different approaches to generalize the trapezoidal method to fractional
differential equations. We analyze the main theoretical properties and we discuss …

We consider numerical methods for solving the fractional-in-space Allen–Cahn equation
which contains small perturbation parameters and strong nonlinearity. A standard fully …

Matrix functions are a central topic of linear algebra, and problems of their numerical
approximation appear increasingly often in scientific computing. We review various rational …

In this paper we apply a high order difference scheme and Galerkin spectral technique for
the numerical solution of multi-term time fractional partial differential equations. The …

In this paper, we firstly develop two high-order approximate formulas for the Riesz fractional
derivative. Secondly, we propose a temporal second order numerical method for a fractional …

The concept of fractional derivative has been demonstrated to be successful when applied
to model a range of physical and real life phenomena, be it in engineering and science …