On a Fuzzy Difference Equation Based on Generalized Division

Abstract

In this work, a second-order fractional fuzzy difference equation is investigated. Firstly, the fuzzy difference equation is transformed into the corresponding ordinary difference equations with parameters based on the fuzzy set theory and generalized division of fuzzy number. And then, the existence and uniqueness of the solution for the ordinary difference equations are proved by the mathematical induction, the mixed iteration method and the inequality technique. Finally, the existence and uniqueness of the solution for the fractional fuzzy difference equation is obtained.