Abstract
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 theΦ-Caputo sense. The numerical method relies on a novel type of operational matrix method, namely, theΦ-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.
Highlights
The history of fractional or noninteger order differential and integral operators can be traced back to the origins of integer order calculus [1]
Fractional differential equations have attracted a lot of attention
The authors of [16] employed a Taylor matrix method to find the numerical solution of problem (3) by taking into account the Caputo fractional derivative
Summary
The history of fractional or noninteger order differential and integral operators can be traced back to the origins of integer order calculus [1]. The authors of [16] employed a Taylor matrix method to find the numerical solution of problem (3) by taking into account the Caputo fractional derivative. This approach is based on a fractional version of Taylor’s formula, which was first proposed in [17]. In [19], a trapezoidal approximation of the fractional integral is used to get the numerical solution of problem (3) with Caputo fractional derivative.
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