Jahan, Shah2026-03-112026-03-112025http://cuh.ndl.gov.in/handle/123456789/1746In 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.en