Stability sets for fractional differential equations with two delays

The main subject of this study is a linear fractional-order differential equation with two delayed terms. By applying the D-decomposition method to the characteristic equation, we present a stability region as a necessary and sufficient condition for the asymptotic stability of the zero solution. Given the relationship between the Caputo fractional derivative and the integer-order derivative, we compare the conditions in this study with the results of the corresponding first-order delay differential equation to demonstrate the validity of the extension.