An approximate approach for fractional relaxation-oscillation equation based on Taylor expansion

Abstract This work presents an application of the efficient method to solve the fractional relaxation-oscillation equation. The method is based on employing Taylor polynomial of degree m for unknown function and repeated integration technique coupled with the Riemann-Liouville fractional derivative such that the fractional relaxation-oscillation equation is transformed into a linear equations system involving an unknown function and its derivatives which is then solved. An error analysis is given along with several numerical applications to demonstrate the simplicity and the effectiveness of the suggested technique for which the exact solutions are known beforehand.