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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 $$\cases D^\alpha x(t)=A_0x(t)+A_1x(t-r)+f(t),\quad & t\ge 0\\ x(t)=\phi(t),\quad t\in[-r,0],\endcases$$ Moreover, sufficient conditions for the finite time stability, for the particular class of fractional time-delay system are obtained.

34K05General theory of functional-differential equations
34K20Stability theory of functional-differential equations
26A33Fractional derivatives and integrals (real functions)
Full Text: DOI
[1] Daftardar-Gdjji, Varsha; Babakhani, A.: Analysis of a system of fractional differential equations. J. math. Anal. appl. 293, 511-522 (2004) · Zbl 1058.34002
[2] Delbosco, Domenico; Rodino, Luigi: Existence and uniqueness for a nonlinear fractional differential equation. J. math. Anal. appl. 204, 609-625 (1996) · Zbl 0881.34005
[3] Diethelm, Kai; Ford, Neville J.: Analysis of fractional differential equations. J. math. Anal. appl. 265, 229-248 (2002) · Zbl 1014.34003
[4] El-Sayed, Ahamed M. A.: On the fractional differential equations. Appl. math. Comput. 49, 205-213 (1992) · Zbl 0757.34005
[5] El-Sayed, Ahamed M. A.: Fractional order differential equation. Kyungpook math. J. 28 (1988)
[6] El-Sayed, Ahamed M. A.: Nonlinear functional differential equations of arbitrary orders. Nonlinear anal. 33, No. 2, 181-186 (1998) · Zbl 0934.34055
[7] Yu, Cheng; Gao, Guozhu: Some results on a class of fractional functional differential equations. Commun. appl. Nonlinear anal. 11, No. 3, 67-75 (2004) · Zbl 1051.34048
[8] Hale, Jack: Theory of functional differential equations. (1997)
[9] Lazarević, M. P.: Finite time stability analysis of PD$\alpha $ fractional control of robotic time-delay systems. Mech. res. Commun. 33, 269-279 (2006) · Zbl 1192.70008
[10] Podlubny, I.: Fractional differential equations. (1999) · Zbl 0924.34008
[11] Miller, K. S.; Ross, B.: An introduction to the fractional calculus and fractional differential equation. (1993) · Zbl 0789.26002
[12] Daftardar-Gejji, Varsha: Positive solutions of a system of a nonautomous fractional differential equations. J. math. Anal. appl. 302, 56-64 (2005) · Zbl 1064.34004