Fibonacciwaveletmethodforthenumericalsolutionofafractional relaxation–oscillationmodel

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.