Given the increasing number of proposals and definitions of operators in the scope of
fractional calculus, it is important to introduce a systematic classification. Nonetheless, many …

Artificial neural network (ANN) is the backbone of machine learning, specifically deep
learning. The interpolating and learning ability of an ANN makes it an ideal tool for …

Fractional calculus, which has two main features—singularity and nonlocality from its origin—
means integration and differentiation of any positive real order or even complex order. It has …

Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …

This paper discusses the concepts underlying the formulation of operators capable of being
interpreted as fractional derivatives or fractional integrals. Two criteria for required by a …

We have demonstrated that both fractional extensions of the standard rotation group SO (N)
based on the Riemann and the Caputo fractional derivative definition respectively may …

A class of second order approximations, called the weighted and shifted Grünwald
difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with …

We examine a numerical method to approximate to a fractional diffusion equation with the
Riesz fractional derivative in a finite domain, which has second order accuracy in time and …

In this paper, a novel compact operator is derived for the approximation of the Riesz
derivative with order α∈(1,2. The compact operator is proved with fourth-order accuracy …

A new method that enables easy and convenient discretization of partial differential
equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays …