Numerical solution of fractional relaxation–oscillation equation by using residual power series method

Geeta Arora, Rajendra Pant, Homan Emaifar, Masoumeh Khademi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


The relaxation oscillator is a type of oscillator that is based on the nature of physical phenomena that tend to return to equilibrium after being distributed. The relaxation–oscillation equation is the primary equation of the process of relaxation–oscillation. In this work, the relaxation–oscillation equation is solved using the residual power series method, which is a fractional order differential equation with defined initial conditions. The results obtained by this method are more reliable and accurate as compared to those obtained by other methods studied previously to solve this equation. The reliability and efficiency of this method are demonstrated by means of three examples with exact solutions compared with approximate solutions by means of errors. The pseudocode of the applied methodology has also been discussed in brief. The residual power series method can be used to solve well-known fractional order differential equations.

Original languageEnglish
Pages (from-to)249-257
Number of pages9
JournalAEJ - Alexandria Engineering Journal
Publication statusPublished - 15 Jul 2023
Externally publishedYes


  • Exact solutions and approximate solutions
  • Fractional differential equations
  • Fractional relaxation–oscillation equation
  • Residual power series method

ASJC Scopus subject areas

  • General Engineering


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