Nonstandard Gauss-Lobatto quadrature approximation to fractional derivatives

DOI10.2478/s13540-014-0215-zzbMath1314.65037OpenAlexW1978195774MaRDI QIDQ2347226

Shahrokh Esmaeili, Gradimir V. Milovanović

Publication date: 27 May 2015

Published in: Fractional Calculus \& Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s13540-014-0215-z

zbMATH Keywords

weightsquadrature rulenodesMathematica packagefractional derivativegaussian quadraturesoftware implementation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Numerical integration (65D30)

Related Items

Approximating the Caputo Fractional Derivative through the Mittag-Leffler Reproducing Kernel Hilbert Space and the Kernelized Adams--Bashforth--Moulton Method, A convergent algorithm for solving higher-order nonlinear fractional boundary value problems, A Jacobi spectral method for calculating fractional derivative based on mollification regularization, On fractional-Legendre spectral Galerkin method for fractional Sturm-Liouville problems, Solving 2D time-fractional diffusion equations by a pseudospectral method and Mittag-Leffler function evaluation, Numerical solution of gas solution in a fluid: fractional derivative model

Uses Software

• Mathematica
• Matlab
• OrthogonalPolynomials
• Chebfun
• OPQ
• Mittag-Leffler
• FastGaussQuadrature
• mlf

Cites Work

• Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials
• Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives
• Nonstandard Gaussian quadrature formulae based on operator values
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Uniform approximation to fractional derivatives of functions of algebraic singularity
• Fractals and fractional calculus in continuum mechanics
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Chebfun and numerical quadrature
• Evaluation of generalized Mittag-Leffler functions on the real line
• Numerical approximation to the fractional derivative operator
• Spectral approximations to the fractional integral and derivative
• Interpolation Processes
• The fundamental solution of the space-time fractional diffusion equation
• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights
• Gaussian-type Quadrature Rules for Müntz Systems
• Error Bounds for the Numerical Integration of Functions with Limited Smoothness
• Calculation of Gauss Quadrature Rules
• Fractional Calculus with Applications in Mechanics
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