Fibonacci wavelet method for the numerical solution of a fractional relaxation–oscillation model

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 operation...

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Bibliographic Details
Main Authors: Shah Jahan, Shahid Ahmed, Pooja Yadav, Kottakkaran Sooppy Nisar
Format: Article
Language:English
Published: Elsevier 2023-12-01
Series:Partial Differential Equations in Applied Mathematics
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S2666818123000815
Description
Summary: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.
ISSN:2666-8181