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 relaxation-oscillation equation. The fractional derivatives in the relaxation-oscillation equations under consideration are defined in the Phi-Caputo sense. The numerical method relies on a novel type of operational matrix method, namely, the Phi-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.