Existence and uniqueness of a class of uncertain Liouville-Caputo fractional difference equations

Abstract

We consider a class of uncertain fractional difference equation of the Liouville-Caputo type (UFLCDE). An equivalent uncertain fractional sum equation is found to the UFLCDE by using the basic properties. The successive Picard iteration method for finding a solution to the UFLCDE is introduced. Using the theory of Banach contraction under the Lipschitz constant condition, we investigate the structure of algebras of existence and uniqueness of the UFLCDE. The article finally exhibits three examples to show the effectiveness of the proposed investigation.