Fixed point

Fixed-point theorem

Applied mathematics

Stability (learning theory)

Computer science

Contraction mapping

Mathematics

Mathematical analysis

Mittag-Leffler function

Artificial neural network

Fractional calculus

Machine learning

Nonlinear Analysis Modelling and Control

A class of semilinear fractional difference equations is introduced in this paper. The fixed point theorem is adopted to find stability conditions for fractional difference equations. The complete solution space is constructed and the contraction mapping is established by use of new equivalent sum equations in form of a discrete Mittag-Leffler function of two parameters. As one of the application, finite-time stability is discussed and compared. Attractivity of fractional difference equations is proved, and Mittag-Leffler stability conditions are provided. Finally, the stability results are applied to fractional discrete-time neural networks with and without delay, which show the fixed point technique’s efficiency and convenience.

Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique