Fractional extreme value adaptive training method: fractional steepest descent approach

Area of Science:

• Fractional calculus applications
• Adaptive learning systems
• Signal processing algorithms

Background:

• Fractional calculus is increasingly applied in signal processing and adaptive learning.
• Existing adaptive learning methods may not fully leverage the benefits of fractional calculus.

Purpose of the Study:

• To propose a novel fractional adaptive learning approach using fractional calculus.
• To introduce and analyze a fractional steepest descent method.
• To investigate the stability and convergence properties of the proposed method.

Main Methods:

• Development of a fractional steepest descent algorithm.
• Study of a fractional quadratic energy norm.
• Theoretical analysis of stability and convergence.
• Numerical implementation and experimental stability analysis.

Main Results:

• A novel fractional steepest descent approach for adaptive learning is presented.
• The stability and convergence of the fractional method are theoretically analyzed.
• Numerical simulations confirm the stability of the proposed fractional steepest descent approach.

Conclusions:

• The proposed fractional steepest descent method offers a promising new direction for adaptive learning and signal processing.
• Fractional calculus provides a powerful framework for enhancing adaptive learning algorithms.
• Further research can explore broader applications of this fractional approach.