An Introduction to Fuzzy Differential Equations

Abstract

This work investigates the existence and uniqueness of solutions for two distinct classes of fuzzy différential equations using Tarski's xed point theorem.Firstly,wean alyze fuzzy différential equations with boundary conditions,focusing on how Tarski's the oremcane stablish theexis- tence of solutions that satisfys peci ed boundary constraints.Secondly,we delvein to Caputo- type erential equations,applying the theorem to demonstrate the existence of unique solutions with in this specialized frame work.By leveraging Tarski's xed point the orem,we establish the oretical foundations that en sure the of solutions in both problem classes.To illustrate our ndings,wepresen wherein thesemethodologiesareappliedtoarealworldscenario,showcasingthee ectiveness and applicabilityofTarski'stheoreminsolvingcomplexfuzzydi erentialequations.Thisex- ample notonlyvalidatesourtheoreticalresultsbutalsounderscoresthepracticalutilityof employing xedpointtheoremsinmathematicalmodelingunderuncertainty.