Numerical approximation to the fractional derivative operator
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Summary
The computation of the contour integral yields a rational approximation to Aα which can be used to define k-step formulas for the numerical integration of Fractional Differential Equations.
- Type
- article
- Published
- 2014-07-01
- Cited by
- 16
- References
- 29
- OpenAlex
- https://openalex.org/W1970786191
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:45890296
Keywords
Mathematics, Discretization, Numerical analysis, Numerical approximation, Fractional calculus
References
- Analysis of Fractional Differential Equations
- Pitfalls in fast numerical solvers for fractional differential equations
- Error of the Newton-Cotes and Gauss-Legendre quadrature formulas
- A Padé Approximation Method for Square Roots of Symmetric Positive Definite Matrices
- Bounds on the error of Gauss-type quadratures
- Discretized fractional calculus
- Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
- Rates of convergence of Gaussian quadrature for singular integrands
- Rough and ready error estimates in Gaussian integration of analytic functions
- On Multistep Methods for Differential Equations of Fractional Order
- Fast numerical solution of weakly singular Volterra integral equations
- Is Gauss Quadrature Better than Clenshaw-Curtis?
- Asymptotic estimates for the error of the Gauss-Legendre quadrature formula
- Rates of convergence of Gauss, Lobattom, and Radau integration rules for singular integrands
- Error estimates for Gauss quadrature formulas for analytic functions
- Algorithms for the matrix pth root
- Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals
- A Schur-Padé Algorithm for Fractional Powers of a Matrix
- A Stability Analysis of Convolution Quadraturea for Abel-Volterra Integral Equations
- Fast and Oblivious Convolution Quadrature
Cited by
- AN APPROXIMATION OF THE FRACTIONAL INTEGRALS USING QUADRATIC INTERPOLATION
- Nonstandard Gauss—Lobatto quadrature approximation to fractional derivatives
- Numerical Caputo Differentiation by Radial Basis Functions
- On the Construction and Properties of m-step Methods for FDEs
- Solving the time-fractional Schrödinger equation by Krylov projection methods
- On the construction of m-step methods for FDEs
- Error bounds and estimates for Krylov subspace approximations of Stieltjes matrix functions
- Efficient Implementation of Rational Approximations to Fractional Differential Operators
- Rational approximations to fractional powers of self-adjoint positive operators
- Dissipativity and Contractivity Analysis for Fractional Functional Differential Equations and their Numerical Approximations
- Limited‐memory polynomial methods for large‐scale matrix functions
- Computational aspects of the geometric mean of two matrices: a survey
- Elements of mathematical phenomenology and analogies of electrical and mechanical oscillators of the fractional type with finite number of degrees of freedom of oscillations: linear and nonlinear modes
- New Class of Complex Models of Materials withPiezoelectric Properties with Differential Constitutive Relations of Fractional Order: An Overview
- DISSIPATIVITY AND CONTRACTIVITY ANALYSIS FOR FRACTIONAL FUNCTIONAL DIFFERENTIAL EQUATIONS AND THEIR NUMERICAL APPROXIMATIONS
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