Fibonacciwaveletmethodforthenumericalsolutionofafractional relaxation–oscillationmodel
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Date
2025
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Abstract
In this paper,wehavediscussed theFibonacciwavelet (FW) framework for numerical simulations of the
fractionalrelaxation–oscillationmodel(FROM).Firstly,thefractionalorderoperationalmatricesofintegration
associatedwiththeFWareconstructedviatheblockpulsefunctions.Theoperationalmatricesmergedwiththe
collocationmethodareusedtoconvertthegivenproblemintoasystemofalgebraicequationsthatissolvedby
theNewtonmethod.Weconducterroranalysis,performnumericalsimulations,andpresentthecorresponding
resultstoestablishthecredibilityandpracticalapplicabilityoftheproposedtechnique.Numericalexamplesare
providedtoshowtheefficiencyofourapproach.Toshowtheaccuracyof theFW-basednumerical technique,
theapproximatesolutionsofFROMarecomparedwiththeexact solutionandotherexistingmethods.This
researchopensupnewpossibilities forusingFWas apowerful tool for addressingcomplexmathematical
problems inreal-worldsystems.