-
1
-
-
0000902727
-
Generalized viscoelastic models: their fractional equations with solutions
-
Schiessel, H., Metzler, R., Blumen, A., Nonenmacher, T.F.: Generalized viscoelastic models: their fractional equations with solutions. J. Phys. A 28, 6567–6584 (1995)
-
(1995)
J. Phys. A
, vol.28
, pp. 6567-6584
-
-
Schiessel, H.1
Metzler, R.2
Blumen, A.3
Nonenmacher, T.F.4
-
2
-
-
84861764006
-
Nonlinear dynamics and chaos in fractional-order neural networks
-
Kaslik, E., Sivasundaram, S.: Nonlinear dynamics and chaos in fractional-order neural networks. Neural Netw. 32, 245–256 (2012)
-
(2012)
Neural Netw.
, vol.32
, pp. 245-256
-
-
Kaslik, E.1
Sivasundaram, S.2
-
4
-
-
84930374284
-
Method of approximate particular solutions for constant-and variable-order fractional diffusion models
-
Fu, Z.J., Chen, W., Ling, L.: Method of approximate particular solutions for constant-and variable-order fractional diffusion models. Eng. Anal. Bound. Elem. 57, 37–46 (2015)
-
(2015)
Eng. Anal. Bound. Elem.
, vol.57
, pp. 37-46
-
-
Fu, Z.J.1
Chen, W.2
Ling, L.3
-
5
-
-
84912570018
-
A relative entropy method to measure non-exponential random data
-
Liang, Y., Chen, W.: A relative entropy method to measure non-exponential random data. Phys. Lett. A 379(3), 95–99 (2014)
-
(2014)
Phys. Lett. A
, vol.379
, Issue.3
, pp. 95-99
-
-
Liang, Y.1
Chen, W.2
-
9
-
-
37349014877
-
Theory of fractional differential inequalities and applications
-
Lakshmikantham, V., Vatsala, A.S.: Theory of fractional differential inequalities and applications. Commun. Appl. Anal. 11, 395–402 (2007)
-
(2007)
Commun. Appl. Anal.
, vol.11
, pp. 395-402
-
-
Lakshmikantham, V.1
Vatsala, A.S.2
-
10
-
-
67349233358
-
-
Cambridge Scientific Publishers, Cambridge
-
Lakshmikantham, V., Leela, S., Vasundhara, D.J.: Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, Cambridge (2009)
-
(2009)
Theory of Fractional Dynamic Systems
-
-
Lakshmikantham, V.1
Leela, S.2
Vasundhara, D.J.3
-
11
-
-
0003598080
-
-
Gordon and Breach Science Publishers, New York
-
Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, New York (1993)
-
(1993)
Fractional Integrals and Derivatives: Theory and Applications
-
-
Samko, S.G.1
Kilbas, A.A.2
Marichev, O.I.3
-
12
-
-
84977656637
-
-
204, Elsevier, Amsterdam
-
Kibas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)
-
(2006)
Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies
-
-
Kibas, A.A.1
Srivastava, H.M.2
Trujillo, J.J.3
-
14
-
-
74149094877
-
Fractional integral inequalities and applications
-
Denton, Z., Vatsala, A.S.: Fractional integral inequalities and applications. Comput. Math. Appl. 59(3), 1087–1094 (2010)
-
(2010)
Comput. Math. Appl.
, vol.59
, Issue.3
, pp. 1087-1094
-
-
Denton, Z.1
Vatsala, A.S.2
-
15
-
-
0002731965
-
Stability results for fractional differential equations with applications to control processing
-
IEEE-SMC, Lille
-
Matignon, D.: Stability results for fractional differential equations with applications to control processing. In: Computational Engineering in Systems and Application IMACS, vol. 2, pp. 963–968. IEEE-SMC, Lille (1996)
-
(1996)
Computational Engineering in Systems and Application IMACS, vol. 2
, pp. 963-968
-
-
Matignon, D.1
-
16
-
-
33947133956
-
Stability analysis of linear fractional differential system with multiple time delays
-
Deng, W., Li, C., Lv, J.: Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn. 48, 409–416 (2007)
-
(2007)
Nonlinear Dyn.
, vol.48
, pp. 409-416
-
-
Deng, W.1
Li, C.2
Lv, J.3
-
17
-
-
84860329588
-
-
Zhang, F., Li, C., Chen, Y.Q.: Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Int. J. Differ. Equ.
-
Zhang, F., Li, C., Chen, Y.Q.: Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Int. J. Differ. Equ. doi:10.1155/2011/635165
-
-
-
-
18
-
-
79953701362
-
A survey on the stability of fractional differential equations
-
Li, C.P., Zhang, F.R.: A survey on the stability of fractional differential equations. Eur. Phys. J. Special Top. 193, 27–47 (2011)
-
(2011)
Eur. Phys. J. Special Top.
, vol.193
, pp. 27-47
-
-
Li, C.P.1
Zhang, F.R.2
-
19
-
-
0031258982
-
Impulsive stabilization for control and synchronization of chaotic systems
-
Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic systems. IEEE Trans. Circuits Syst. I 44(10), 967–988 (1997)
-
(1997)
IEEE Trans. Circuits Syst. I
, vol.44
, Issue.10
, pp. 967-988
-
-
Yang, T.1
Chua, L.O.2
-
20
-
-
33744519669
-
-
Hindawi Publishing Corporation, New York
-
Benchohra, M., Henderson, J., Ntouyas, S.: Impulsive Differential Equations and Inclusions. Hindawi Publishing Corporation, New York (2006)
-
(2006)
Impulsive Differential Equations and Inclusions
-
-
Benchohra, M.1
Henderson, J.2
Ntouyas, S.3
-
21
-
-
34648879326
-
-
Princeton University Press, Princeton
-
Haddad, W.M., Chellaboina, V., Nersesov, S.G.: Impulsive and Hybrid Dynamical Systems. Princeton University Press, Princeton (2006)
-
(2006)
Impulsive and Hybrid Dynamical Systems
-
-
Haddad, W.M.1
Chellaboina, V.2
Nersesov, S.G.3
-
22
-
-
84856291615
-
On the concept and existence of solution for impulsive fractional differential equations
-
Fĕckan, M., Zhou, Y., Wang, J.R.: On the concept and existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 3050–3060 (2012)
-
(2012)
Commun. Nonlinear Sci. Numer. Simul.
, vol.17
, pp. 3050-3060
-
-
Fĕckan, M.1
Zhou, Y.2
Wang, J.R.3
-
23
-
-
84868207712
-
Impulsive fractional functional differential equations
-
Guo, T.L., Jiang, W.: Impulsive fractional functional differential equations. Comput. Math. Appl. 64(10), 3414–3424 (2012)
-
(2012)
Comput. Math. Appl.
, vol.64
, Issue.10
, pp. 3414-3424
-
-
Guo, T.L.1
Jiang, W.2
-
24
-
-
84868209436
-
Controllability and observability of impulsive fractional linear time-invariant system
-
Guo, T.L.: Controllability and observability of impulsive fractional linear time-invariant system. Comput. Math. Appl. 64, 3171–3182 (2012)
-
(2012)
Comput. Math. Appl.
, vol.64
, pp. 3171-3182
-
-
Guo, T.L.1
-
25
-
-
84865640170
-
Nonlinear impulsive problems for fractional differential equations and Ulam stability
-
Wang, J.R., Fĕckan, M., Zhou, Y.: Nonlinear impulsive problems for fractional differential equations and Ulam stability. Comput. Math. Appl. 64, 3389–3405 (2012)
-
(2012)
Comput. Math. Appl.
, vol.64
, pp. 3389-3405
-
-
Wang, J.R.1
Fĕckan, M.2
Zhou, Y.3
-
26
-
-
0003816483
-
-
Springer, New York
-
Ge, S.S., Hang, C.C., Lee, T.H., Zhang, T.: Stable adaptive neural network control. Springer, New York (2010)
-
(2010)
Stable adaptive neural network control
-
-
Ge, S.S.1
Hang, C.C.2
Lee, T.H.3
Zhang, T.4
-
27
-
-
85028172044
-
Adaptive neural networks tracking control of uncertain nonlinear discrete-time systems with nonaffine dead-zone input
-
Liu, Y.J., Tong, S.C.: Adaptive neural networks tracking control of uncertain nonlinear discrete-time systems with nonaffine dead-zone input. IEEE Trans. Cybern. 45(3), 497–505 (2015)
-
(2015)
IEEE Trans. Cybern.
, vol.45
, Issue.3
, pp. 497-505
-
-
Liu, Y.J.1
Tong, S.C.2
-
28
-
-
84902164335
-
Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash
-
Liu, Y.J., Tong, S.C.: Adaptive fuzzy control for a class of nonlinear discrete-time systems with backlash. IEEE Trans. Fuzzy Syst. 22(5), 1359–1365 (2014)
-
(2014)
IEEE Trans. Fuzzy Syst.
, vol.22
, Issue.5
, pp. 1359-1365
-
-
Liu, Y.J.1
Tong, S.C.2
-
29
-
-
79960150696
-
Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems
-
Liu, Y.J., Chen, C.L.P., Wen, G.X., Tong, S.C.: Adaptive neural output feedback tracking control for a class of uncertain discrete-time nonlinear systems. IEEE Trans. Neural Netw. 22(7), 1162–1167 (2011)
-
(2011)
IEEE Trans. Neural Netw.
, vol.22
, Issue.7
, pp. 1162-1167
-
-
Liu, Y.J.1
Chen, C.L.P.2
Wen, G.X.3
Tong, S.C.4
-
30
-
-
0022098324
-
An Introductory survey of fuzzy control
-
Sugeno, M.: An Introductory survey of fuzzy control. Inf. Sci. 36(1), 59–83 (1985)
-
(1985)
Inf. Sci.
, vol.36
, Issue.1
, pp. 59-83
-
-
Sugeno, M.1
-
31
-
-
0033721189
-
Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach
-
Cao, Y.Y., Frank, P.M.: Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach. IEEE Trans. Fuzzy Syst. 8(2), 200–211 (2000)
-
(2000)
IEEE Trans. Fuzzy Syst.
, vol.8
, Issue.2
, pp. 200-211
-
-
Cao, Y.Y.1
Frank, P.M.2
-
32
-
-
41849148660
-
Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: A new approach
-
Kruszewski, A., Wang, R., Guerra, T.M.: Nonquadratic stabilization conditions for a class of uncertain nonlinear discrete time TS fuzzy models: A new approach. IEEE Trans. Automatic Control 53(2), 606–611 (2008)
-
(2008)
IEEE Trans. Automatic Control
, vol.53
, Issue.2
, pp. 606-611
-
-
Kruszewski, A.1
Wang, R.2
Guerra, T.M.3
-
33
-
-
84871749893
-
Stability and stabilization of fractional order linear systems with convex polytopic uncertainties
-
Lu, J.G., Chen, Y.Q.: Stability and stabilization of fractional order linear systems with convex polytopic uncertainties. Fract. Calc. Appl. Anal. 16(1), 142–157 (2013)
-
(2013)
Fract. Calc. Appl. Anal.
, vol.16
, Issue.1
, pp. 142-157
-
-
Lu, J.G.1
Chen, Y.Q.2
-
34
-
-
80051682888
-
Stability analysis of fractional-order systems with double noncommensurate orders for matrix case
-
Jiao, Z., Chen, Y.Q.: Stability analysis of fractional-order systems with double noncommensurate orders for matrix case. Fract. Calc. Appl. Anal. 14(3), 436–453 (2011)
-
(2011)
Fract. Calc. Appl. Anal.
, vol.14
, Issue.3
, pp. 436-453
-
-
Jiao, Z.1
Chen, Y.Q.2
-
35
-
-
84881466704
-
-
Chen, H., Chen, W., Zhang, B.W., Cao, H.T.: Robust synchronization of incommensurate fractional-order chaotic systems via second-order sliding mode technique. J. Appl. Math.
-
Chen, H., Chen, W., Zhang, B.W., Cao, H.T.: Robust synchronization of incommensurate fractional-order chaotic systems via second-order sliding mode technique. J. Appl. Math. doi:10.1155/2013/321253
-
-
-
-
36
-
-
84879658302
-
Almost sure and moment stability properties of fractional order Black-Scholes model
-
Zeng, C.B., Chen, Y.Q., Yang, Q.G.: Almost sure and moment stability properties of fractional order Black-Scholes model. Fract. Calc. Appl. Anal. 16(2), 317–331 (2013)
-
(2013)
Fract. Calc. Appl. Anal.
, vol.16
, Issue.2
, pp. 317-331
-
-
Zeng, C.B.1
Chen, Y.Q.2
Yang, Q.G.3
-
37
-
-
76449092011
-
Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability
-
Li, Y., Chen, Y.Q., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Comput. Math. Appl. 59, 1810–1821 (2010)
-
(2010)
Comput. Math. Appl.
, vol.59
, pp. 1810-1821
-
-
Li, Y.1
Chen, Y.Q.2
Podlubny, I.3
-
38
-
-
84860329588
-
-
Zhang, F.R., Li, C.P., Chen, Y.Q.: Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Int. J. Differ. Equ.
-
Zhang, F.R., Li, C.P., Chen, Y.Q.: Asymptotical stability of nonlinear fractional differential system with Caputo derivative. Int. J. Differ. Equ. doi:10.1155/2011/635165
-
-
-
-
39
-
-
84858841611
-
Stability analysis of Caputo fractional order nonlinear systems revisited
-
Delavari, H., Baleanu, D., Sadati, J.: Stability analysis of Caputo fractional order nonlinear systems revisited. Nonlinear Dyn. 67, 2433–2439 (2012)
-
(2012)
Nonlinear Dyn.
, vol.67
, pp. 2433-2439
-
-
Delavari, H.1
Baleanu, D.2
Sadati, J.3
-
40
-
-
84891556704
-
Stability analysis for nonlinear fractional-order systems based on comparison principle
-
Wang, Z.L., Yang, D., Ma, T., Sun, N.: Stability analysis for nonlinear fractional-order systems based on comparison principle. Nonlinear Dyn. 75, 387–402 (2014)
-
(2014)
Nonlinear Dyn.
, vol.75
, pp. 387-402
-
-
Wang, Z.L.1
Yang, D.2
Ma, T.3
Sun, N.4
-
41
-
-
84899095856
-
Global stability of impulsive fractional differential equations
-
Stamova, I.: Global stability of impulsive fractional differential equations. Appl. Math. Comput. 237, 605–612 (2014)
-
(2014)
Appl. Math. Comput.
, vol.237
, pp. 605-612
-
-
Stamova, I.1
-
42
-
-
84885182412
-
Stability analysis of impulsive functional systems of fractional order
-
Stamova, I., Stamov, G.: Stability analysis of impulsive functional systems of fractional order. Commun. Nonlinear Sci. Numer. Simul. 19(3), 702–709 (2014)
-
(2014)
Commun. Nonlinear Sci. Numer. Simul.
, vol.19
, Issue.3
, pp. 702-709
-
-
Stamova, I.1
Stamov, G.2
-
43
-
-
84987871759
-
Algebraic stability of impulsive fractional-order systems
-
Wu, R.C., Hei, X.D.: Algebraic stability of impulsive fractional-order systems. Electron. J. Qual Theory Differ. Equ. 32, 1–13 (2014)
-
(2014)
Electron. J. Qual Theory Differ. Equ.
, vol.32
, pp. 1-13
-
-
Wu, R.C.1
Hei, X.D.2
-
44
-
-
85067857168
-
-
World Scientific Publishing, Singapore
-
Caponetto, R., Doongola, G., Fortuna, L., Petráš, I.: Fractional Order Systems: Modeling and Control Applications. World Scientific Publishing, Singapore (2010)
-
(2010)
Fractional Order Systems: Modeling and Control Applications
-
-
Caponetto, R.1
Doongola, G.2
Fortuna, L.3
Petráš, I.4
-
46
-
-
78650513186
-
-
Springer, Berlin
-
Baleanu, D., Güvenc, Z.B., Machado, J.A.T.: New Trends in Nanotechnology and Fractional Calculus Applications. Springer, Berlin (2010)
-
(2010)
New Trends in Nanotechnology and Fractional Calculus Applications
-
-
Baleanu, D.1
Güvenc, Z.B.2
Machado, J.A.T.3
-
47
-
-
77954349836
-
Stability of fractional-order systems with rational orders: a survey
-
Petráš, I.: Stability of fractional-order systems with rational orders: a survey. Fract. Calc. Appl. Anal. 12(3), 269–298 (2009)
-
(2009)
Fract. Calc. Appl. Anal.
, vol.12
, Issue.3
, pp. 269-298
-
-
Petráš, I.1
-
48
-
-
0002324637
-
Vector Lyapunov functions
-
Bellman, R.: Vector Lyapunov functions. SIAM J. Control 1, 32–34 (1962)
-
(1962)
SIAM J. Control
, vol.1
, pp. 32-34
-
-
Bellman, R.1
-
49
-
-
4544370392
-
Method of vector Lyapunov functions of interconnected systems with distributed parameters (survey) (in Russian)
-
Matrosov, V.M.: Method of vector Lyapunov functions of interconnected systems with distributed parameters (survey) (in Russian). Avtomatika i Telemekhanika 33, 63–75 (1972)
-
(1972)
Avtomatika i Telemekhanika
, vol.33
, pp. 63-75
-
-
Matrosov, V.M.1
-
50
-
-
33244457608
-
On the stability and control of nonlinear dynamical systems via vector Lyapunov functions
-
Nersesov, S.G., Haddad, W.M.: On the stability and control of nonlinear dynamical systems via vector Lyapunov functions. IEEE Trans. Automatic Control 15(2), 203–215 (2006)
-
(2006)
IEEE Trans. Automatic Control
, vol.15
, Issue.2
, pp. 203-215
-
-
Nersesov, S.G.1
Haddad, W.M.2
-
51
-
-
80052654574
-
-
Haubold, H.J., Mathai, A.M., Saxena, R.K.: Mittag–Leffler functions and their applications. J. Appl. Math.
-
Haubold, H.J., Mathai, A.M., Saxena, R.K.: Mittag–Leffler functions and their applications. J. Appl. Math. doi:10.1155/2011/298628
-
-
-
-
52
-
-
84922721300
-
-
Springer, Berlin
-
Gorenflo, R., Kibas, A., Mainardi, F., Rogosin, S.: Mittag–Leffler Functions and Related Topics and Applications. Springer, Berlin (2014)
-
(2014)
Mittag–Leffler Functions and Related Topics and Applications
-
-
Gorenflo, R.1
Kibas, A.2
Mainardi, F.3
Rogosin, S.4
-
53
-
-
0004178386
-
-
Printice Hall, Upper Saddle River
-
Khalil, H.K.: Nonlinear Systems, 3rd edn. Printice Hall, Upper Saddle River (2002)
-
(2002)
Nonlinear Systems
-
-
Khalil, H.K.1
-
54
-
-
0013301123
-
-
Peking University Press, Beijing
-
Huang, L.: Stability Theory. Peking University Press, Beijing (1992)
-
(1992)
Stability Theory
-
-
Huang, L.1
-
55
-
-
84897050571
-
Lyapunov functions for fractional order systems
-
Norelys, A.C., Manuel, A.D., Javier, A.G.: Lyapunov functions for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 19, 2951–2957 (2014)
-
(2014)
Commun. Nonlinear Sci. Numer. Simul.
, vol.19
, pp. 2951-2957
-
-
Norelys, A.C.1
Manuel, A.D.2
Javier, A.G.3
|