Numerical Solution of the Fractional Relaxation-Oscillation Equation by Using Reproducing Kernel Hilbert Space Method

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Tarih

2021

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Springer

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

In this article, the reproducing kernel Hilbert space is proposed and analyzed for the relaxation-oscillation equation of fractional order (FROE). The relaxation oscillation is a type of oscillator based on the way that the physical system’s returns to its equilibrium after being disturbed. We make use of the Caputo fractional derivative. The approximate solution can be obtained by taking n-terms of the analytical solution that is in term of series formula. The numerical experiments are used to prove the convergence of the approximate solution to the analytical solution. The results obtained by the given method demonstrate that it is convenient and efficient for FROE. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited.

Açıklama

Anahtar Kelimeler

Caputo derivative, Fractional relaxation-oscillation equation, Hilbert space, Inner product, Numerical approximation, Reproducing kernel Hilbert space method

Kaynak

International Journal of Applied and Computational Mathematics

WoS Q Değeri

Scopus Q Değeri

Q2

Cilt

7

Sayı

4

Künye