Stability analysis of a class of fractional delay differential equations

In this paper we analyse stability of nonlinear fractional order delay differential equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$D^{\alpha} y(t) = a f\left(y(t-\tau)\right) - b y(t)$\end{document}, where Dα is a Caputo fractional derivative of order 0 < α ≤ 1. We describe stability regions using critical curves. To explain the proposed theory, we discuss fractional order logistic equation with delay.