Stability Analysis of Fractional Differential System with Constant Delay

In this work, we analyze the stability of nonlinear fractional order delay differential equations of the form ^CD^1/2x(t) = ax(t) + bx(t-1)x(t)+f(t, x(t)), where ^CD^1/2 is a Caputo fractional derivative of order 1/2. Some numerical illustrations are provided to explain the proposed theory, by giving conditions on the non-linear term f(t, x(t)).