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Approximating the Caputo fractional derivative through the Mittag-Leffler reproducing kernel Hilbert space and the kernelized Adams-Bashforth-Moulton method. (English) Zbl 1375.26018

The authors introduce techniques for the estimation of solutions of fractional differential equations and the approximation of a function’s Caputo fractional derivative. These techniques are based on scattered data interpolation via reproducing kernel Hilbert spaces which are used for the purpose of estimating fractional derivatives of the Mittag-Leffler function.

MSC:

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

Software:

Mittag-Leffler
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Full Text: DOI

References:

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