Uncertain fractional forward difference equations for Riemann–Liouville type

Abstract

Abstract To model complex systems with discrete-time features and memory effects in the uncertain environment, a definition of an uncertain fractional forward difference equation with Riemann–Liouville-like forward difference is introduced. Moreover, analytic solutions to a type of special linear uncertain fractional difference equations are presented by the Picard iteration method. Then, an existence and uniqueness theorem of the solutions is proved by applying Banach contraction mapping theorem. Finally, two examples are provided to illustrate the validity of the existence and uniqueness theorem.

Keywords

• Discrete fractional calculus
• Uncertainty theory
• Fractional forward difference equations