Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model
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Date
2023-10
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Abstract
In this paper, we have discussed the Fibonacci wavelet (FW) framework for numerical simulations of the
fractional relaxation–oscillation model (FROM). Firstly, the fractional order operational matrices of integration
associated with the FW are constructed via the block pulse functions. The operational matrices merged with the
collocation method are used to convert the given problem into a system of algebraic equations that is solved by
the Newton method. We conduct error analysis, perform numerical simulations, and present the corresponding
results to establish the credibility and practical applicability of the proposed technique. Numerical examples are
provided to show the efficiency of our approach. To show the accuracy of the FW-based numerical technique,
the approximate solutions of FROM are compared with the exact solution and other existing methods. This
research opens up new possibilities for using FW as a powerful tool for addressing complex mathematical
problems in real-world systems.