Attia, NourhaneAkgül, AliSeba, DjamilaNour, Abdelkader2024-12-242024-12-2420212349-5103https://doi.org10.1007/s40819-021-01087-2https://hdl.handle.net/20.500.12604/4024In 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.eninfo:eu-repo/semantics/closedAccessCaputo derivativeFractional relaxation-oscillation equationHilbert spaceInner productNumerical approximationReproducing kernel Hilbert space methodArticle74Q22-s2.0-8511140707410.1007/s40819-021-01087-2