Φ-Haar Wavelet Operational Matrix Method for Fractional Relaxation-Oscillation Equations Containing Φ-Caputo Fractional Derivative

This paper proposes a numerical method for solving fractional relaxation-oscillation equations. A relaxation oscillator is a type of oscillator that is based on how a physical system returns to equilibrium after being disrupted. The primary equation of relaxation and oscillation processes is the rel...

Full description

Saved in:
Bibliographic Details
Published inJournal of function spaces Vol. 2021; pp. 1 - 14
Main Authors Sunthrayuth, Pongsakorn, Aljahdaly, Noufe H., Ali, Amjid, Shah, Rasool, Mahariq, Ibrahim, Tchalla, Ayékotan M. J.
Format Journal Article
LanguageEnglish
Published New York Hindawi 2021
Hindawi Limited
Subjects
Approximation
Computer applications
Linear algebra
Mathematical analysis
Mathematical functions
Mathematical models
Numerical methods
Relaxation oscillators
Online AccessGet full text

Cover

More Information
Summary:This paper proposes a numerical method for solving fractional relaxation-oscillation equations. A relaxation oscillator is a type of oscillator that is based on how a physical system returns to equilibrium after being disrupted. The primary equation of relaxation and oscillation processes is the relaxation-oscillation equation. The fractional derivatives in the relaxation-oscillation equations under consideration are defined in the Φ-Caputo sense. The numerical method relies on a novel type of operational matrix method, namely, the Φ-Haar wavelet operational matrix method. The operational matrix approach has a lower computational complexity. The proposed scheme simplifies the main problem to a set of linear algebraic equations. Numerical examples demonstrate the validity and applicability of the proposed technique.
ISSN:2314-8896
2314-8888
DOI:10.1155/2021/7117064