Approximating the Caputo Fractional Derivative through the Mittag-Leffler Reproducing Kernel Hilbert Space and the Kernelized Adams--Bashforth--Moulton Method

DOI10.1137/16M1056894zbMath1375.26018OpenAlexW2617733559MaRDI QIDQ5347537

Joel A. Rosenfeld, Warren E. Dixon

Publication date: 24 May 2017

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/16m1056894

zbMATH Keywords

numerical differentiationfractional differential equationsfractional derivatives and integralsapplication to differential and integral equations

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12) Numerical differentiation (65D25) Applications of functional analysis to differential and integral equations (46N20) Fractional ordinary differential equations (34A08)

Related Items (10)

A NUMERICAL SCHEME BASED ON TWO- AND THREE-STEP NEWTON INTERPOLATION POLYNOMIALS FOR FRACTAL–FRACTIONAL VARIABLE ORDERS CHAOTIC ATTRACTORS ⋮ A hybrid kernel functions collocation approach for boundary value problems with Caputo fractional derivative ⋮ An accurate numerical technique for fractional oscillation equations with oscillatory solutions ⋮ Modeling the dynamics of nutrient-phytoplankton-zooplankton system with variable-order fractional derivatives ⋮ Approximation methods for solving fractional equations ⋮ The Mittag Leffler reproducing kernel Hilbert spaces of entire and analytic functions ⋮ Weighted composition operators on the Mittag-Leffler spaces of entire functions ⋮ Convergence rate estimates for the kernelized predictor corrector method for fractional order initial value problems ⋮ Heisenberg’s uncertainty principle associated with the Caputo fractional derivative ⋮ Exponential sum approximation for Mittag-Leffler function and its application to fractional Zener wave equation

Uses Software

• Mittag-Leffler

Cites Work

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