Related papers: differint: A Python Package for Numerical Fraction…
In this article we would like to consider some approaches to non-integer integro-differentiations and its implementation in computer algebra system Wolfram Mathematics.
In this paper, an easy-to-implement and computationally effective numerical method based on the new orthogonal hybrid functions is developed to solve system of fractional order differential equations numerically. The new orthogonal hybrid…
Package managers are legion. Every programming language and operating system has its own solution, each with subtly different semantics for dependency resolution. This fragmentation prevents multilingual projects from expressing precise…
Refinement calculus provides a structured framework for the progressive and modular development of programs, ensuring their correctness throughout the refinement process. This paper introduces a refinement calculus tailored for quantum…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
Automatic differentiation plays a prominent role in scientific computing and in modern machine learning, often in the context of powerful programming systems. The relation of the various embodiments of automatic differentiation to the…
The direpack package aims to establish a set of modern statistical dimension reduction techniques into the Python universe as a single, consistent package. The dimension reduction methods included resort into three categories: projection…
We propose a method to numerically compute fractional derivatives (or the fractional Laplacian) on the whole real line via Riesz fractional integrals. The compactified real line is divided into a number of intervals, thus amounting to a…
We present a new version of TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding…
The goal of this work is to discuss how should we impose initial values in fractional problems to ensure that they have exactly one smooth unique solution, where smooth simply means that the solution lies in a certain suitable space of…
We present a simple functional programming language, called Dual PCF, that implements forward mode automatic differentiation using dual numbers in the framework of exact real number computation. The main new feature of this language is the…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
Numerical solving differential equations with fractional derivatives requires elimination of the singularity which is inherent in the standard definition of fractional derivatives. The method of integration by parts to eliminate this…
In this note, a numerical method based on finite differences to solve a class of nonlinear advection-diffusion fractional differential equation is proposed. The fractional operator considered here is the fractional Riemann-Liouville…
The following material was created with the idea of being used for an introductory fractional calculus course. A recapitulation of the history of fractional calculus is presented, as well as the different attempts at fractional derivatives…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
The following document presents some novel numerical methods valid for one and several variables, which using the fractional derivative, allow to find solutions for some non-linear systems in the complex space using real initial conditions.…
This article describes the implementation in the software package NumGfun of classical algorithms that operate on solutions of linear differential equations or recurrence relations with polynomial coefficients, including what seems to be…
In the context of the analysis of measured data, one is often faced with the task to differentiate data numerically. Typically, this occurs when measured data are concerned or data are evaluated numerically during the evolution of partial…
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville…