Fractional Discrete Neural Networks
Description
This book offers a comprehensive guide to Fractional Discrete Neural Networks, delving into their mathematical foundations, stability, solvability, and chaotic dynamics. By combining rigorous analytical approaches with practical numerical simulations, it illuminates how fractional derivatives can enhance neural network modeling, particularly for systems influenced by memory and hereditary effects. Readers will discover cutting-edge methods for assessing network behavior and stability, along with robust simulation techniques. The book's diverse applications span image and signal processing, pattern recognition, artificial intelligence, and data science, showcasing the potential of fractional models to outperform traditional methods in tasks requiring precision and adaptability.
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Persons
Dr. Omar Naifar is an Associate Professor in Electrical Engineering at the Higher Institute of Applied Sciences and Technology in Kairouan, with a strong research focus on control theory, fractional-order systems, and observer design.
Content
Introduction to Fractional Discrete Neural Networks.- Mathematical Foundations of Fractional Calculus in Discrete Time.- Fractional Discrete Neural Network Models: An Overview.- Solvability of Fractional Discrete Neural Networks.- Stability Analysis in Fractional Discrete Systems.- Chaos Theory in Fractional Discrete Neural Networks.- Analytical Approaches to Solvability and Stability.- Numerical Methods for Fractional Discrete Neural Networks.- Fractional Hopfield Neural Networks: Analysis and Applications.- Fractional Discrete Recurrent Neural Networks.- Applications in Image Processing and Pattern Recognition.- Applications in Signal Processing and Time Series Forecasting.- Software and Tools for Simulating Fractional Discrete Neural Networks.- Future Directions and Open Problems in Fractional Discrete Neural Networks.