أ.م.د./ أسامة معاذ رفاعيأ.د./ المتولي محمد العباسي2025-12-162025-12-16https://dspace.academy.edu.ly/handle/123456789/1848In recentyears,researchontheoscillatoryandasymptoticbehaviorofdifferen- tial equationshassignificantlyexpandedduetoitsessentialroleinmodeling phenomena acrossvariousfieldssuchasphysics,biology,andengineering.This thesis contributestothestudyoffunctionaldifferentialequations,withapartic- ular focusonthird-orderdifferentialequationswithdelays,especiallyneutral differential equations.Theprimaryobjectiveistodevelopnewcriteriaforde- termining theoscillationandasymptoticpropertiesoftheseequationsunder different conditions.A differentialequationisamathematicalequationthatdescribesthebehavior of asystembyrepresentingtherelationshipsbetweenvariablesandtheirrates of change.Theseequationsallowustounderstandhowasystemevolvesand predict itsfuturestates.Theyareusedacrossdiversefieldssuchasphysics, engineering,economics,andbiologytomodeldynamicphenomena.Some properties of delay differentia