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Some results of linear fractional order time-delay system. (English) Zbl 1138.34328

Summary: We prove existence and uniqueness theorems for
\[ \begin{cases} D^\alpha x(t)=A_0x(t)+A_1x(t-r)+f(t),\quad & t\geq 0\\ x(t)=\phi(t),\quad t\in[-r,0],\end{cases} \]
Moreover, sufficient conditions for the finite time stability, for the particular class of fractional time-delay system are obtained.

MSC:

34K05 General theory of functional-differential equations
34K20 Stability theory of functional-differential equations
26A33 Fractional derivatives and integrals
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