IEEE Trans Neural Netw Learn Syst. 2015 Apr;26(4):653-62. doi: 10.1109/TNNLS.2013.2286175. Epub 2013 Oct 30.
The application of fractional calculus to signal processing and adaptive learning is an emerging area of research. A novel fractional adaptive learning approach that utilizes fractional calculus is presented in this paper. In particular, a fractional steepest descent approach is proposed. A fractional quadratic energy norm is studied, and the stability and convergence of our proposed method are analyzed in detail. The fractional steepest descent approach is implemented numerically and its stability is analyzed experimentally.
分数微积分在信号处理和自适应学习中的应用是一个新兴的研究领域。本文提出了一种利用分数微积分的新型分数自适应学习方法。具体来说，提出了一种分数最陡下降方法。研究了分数二次能量范数，并详细分析了我们提出的方法的稳定性和收敛性。分数最陡下降方法在数值上实现，并通过实验分析其稳定性。
