A review of definitions of fractional derivatives and other operators
GS Teodoro, JAT Machado, EC De Oliveira - Journal of Computational …, 2019 - Elsevier
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 …
fractional calculus, it is important to introduce a systematic classification. Nonetheless, many …
A survey of fractional calculus applications in artificial neural networks
M Joshi, S Bhosale, VA Vyawahare - Artificial Intelligence Review, 2023 - Springer
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 …
learning. The interpolating and learning ability of an ANN makes it an ideal tool for …
[图书][B] Theory and numerical approximations of fractional integrals and derivatives
C Li, M Cai - 2019 - SIAM
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 …
means integration and differentiation of any positive real order or even complex order. It has …
Numerical methods for nonlocal and fractional models
Partial differential equations (PDEs) are used with huge success to model phenomena
across all scientific and engineering disciplines. However, across an equally wide swath …
across all scientific and engineering disciplines. However, across an equally wide swath …
What is a fractional derivative?
MD Ortigueira, JAT Machado - Journal of computational Physics, 2015 - Elsevier
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 …
interpreted as fractional derivatives or fractional integrals. Two criteria for required by a …
[图书][B] Fractional calculus: an introduction for physicists
R Herrmann - 2011 - World Scientific
Up to now we have introduced a fractional derivative definition for special simple function
classes. In the following section we will present common generalizations for arbitrary …
classes. In the following section we will present common generalizations for arbitrary …
A class of second order difference approximations for solving space fractional diffusion equations
A class of second order approximations, called the weighted and shifted Grünwald
difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with …
difference (WSGD) operators, are proposed for Riemann-Liouville fractional derivatives, with …
Crank–Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
C Çelik, M Duman - Journal of computational physics, 2012 - Elsevier
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 …
Riesz fractional derivative in a finite domain, which has second order accuracy in time and …
A fourth-order compact ADI scheme for two-dimensional nonlinear space fractional Schrodinger equation
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 …
derivative with order α∈(1,2. The compact operator is proved with fourth-order accuracy …