[1] |
Agarwal, R.P., Benchohra, M., Hamani, S.: A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109(3), 973-1033 (2010) · Zbl 1198.26004 · doi:10.1007/s10440-008-9356-6 |
[2] |
Baleanu, D., Jajarmi, A., Asad, J.H.: Classical and fractional aspects of two coupled pendulums. Rom. Rep. Phys. 71(1), Article ID 103 (2019) |
[3] |
Baleanu, D., Ranjbar, A.N., Sadati, S.J.R., Delavari, H., Abdeljawad, T., Gejji, V.: Lyapunov-Krasovskii stability theorem for fractional systems with delay. Rom. J. Phys. 56(5-6), 636-643 (2011) · Zbl 1231.34005 |
[4] |
Baleanu, D., Sajjadi, S.S., Jajarmi, A., Asad, J.H.: New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator. Eur. Phys. J. Plus 134, Article ID 181 (2019) · doi:10.1140/epjp/i2019-12561-x |
[5] |
Chen, L., He, Y., Chai, Y., Wu, R.: New results on stability stabilization of a class of nonlinear fractional-order systems. Nonlinear Dyn. 75(4), 633-641 (2014) · Zbl 1283.93138 · doi:10.1007/s11071-013-1091-5 |
[6] |
Deng, J., Deng, Z.: Existence of solutions of initial value problems for nonlinear fractional differential equations. Appl. Math. Lett. 32, 6-12 (2014) · Zbl 1315.34011 · doi:10.1016/j.aml.2014.02.001 |
[7] |
Deng, W., Li, C., Lu, J.: Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn. 48(4), 409-416 (2007) · Zbl 1185.34115 · doi:10.1007/s11071-006-9094-0 |
[8] |
Diethelm, K.: The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type. Springer, Berlin (2010) · Zbl 1215.34001 · doi:10.1007/978-3-642-14574-2 |
[9] |
Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., Castro-Linares, R.: Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 22, 650-659 (2015) · Zbl 1333.34007 · doi:10.1016/j.cnsns.2014.10.008 |
[10] |
Hale, J., Lunel, S.V.: Introduction to Functional Differential Equations. Springer, New York (1993) · Zbl 0787.34002 · doi:10.1007/978-1-4612-4342-7 |
[11] |
Hajipour, M., Jajarmi, A., Baleanu, D., Sun, H.G.: On an accurate discretization of a variable-order fractional reaction-diffusion equation. Commun. Nonlinear Sci. Numer. Simul. 69, 119-133 (2019) · Zbl 1509.65071 · doi:10.1016/j.cnsns.2018.09.004 |
[12] |
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Application of Fractional Differential Equations. Elsevier, New York (2006) · Zbl 1092.45003 |
[13] |
Li, H., Zhou, S, Li, H.: Asymptotic stability analysis of fractional-order neutral systems with time delay. Adv. Differ. Equ. 2015, Article ID 325 (2015) · Zbl 1422.34046 · doi:10.1186/s13662-015-0659-4 |
[14] |
Liu, K., Jiang, W.: Stability of fractional neutral systems. Adv. Differ. Equ. 2014, Article ID 78 (2014) · Zbl 1417.34176 · doi:10.1186/1687-1847-2014-78 |
[15] |
Liu, S., Jiang, W., Li, X., Zhou, X.F.: Lyapunov stability analysis of fractional nonlinear systems. Appl. Math. Lett. 51, 13-19 (2016) · Zbl 1356.34061 · doi:10.1016/j.aml.2015.06.018 |
[16] |
Liu, S., Wu, X., Zhang, Y.-J., Yang, R.: Asymptotical stability of Riemann-Liouville fractional neutral systems. Appl. Math. Lett. 69, 168-173 (2017) · Zbl 1375.34116 · doi:10.1016/j.aml.2017.02.016 |
[17] |
Liu, S., Wu, X., Zhou, X.F., Jiang, W.: Asymptotical stability of Riemann-Liouville fractional nonlinear systems. Nonlinear Dyn. 86(1), 65-71 (2016) · Zbl 1349.34013 · doi:10.1007/s11071-016-2872-4 |
[18] |
Liu, S., Zhou, X.F., Li, X., Jiang, W.: Stability of fractional nonlinear singular systems its applications in synchronization of complex dynamical networks. Nonlinear Dyn. 84(4), 2377-2385 (2016) · Zbl 1355.34083 · doi:10.1007/s11071-016-2651-2 |
[19] |
Liu, S., Zhou, X.F., Li, X., Jiang, W.: Asymptotical stability of Riemann-Liouville fractional singular systems with multiple time-varying delays. Appl. Math. Lett. 65, 32-39 (2017) · Zbl 1356.34078 · doi:10.1016/j.aml.2016.10.002 |
[20] |
Lu, J.G., Chen, G.: Robust stability and stabilization of fractional-order interval systems: an LMI approach. IEEE Trans. Autom. Control 54(6), 1294-1299 (2009) · Zbl 1367.93472 · doi:10.1109/TAC.2009.2013056 |
[21] |
Matignon, D., Stability results on fractional differential equations with applications to control processing, 963-968 (1996) |
[22] |
Mohammadi, F., Moradi, L., Baleanu, D., Jajarmi, A.: A hybrid functions numerical scheme for fractional optimal control problems: application to non-analytic dynamical systems. J. Vib. Control 24(21), 5030-5043 (2018) |
[23] |
Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999) · Zbl 0924.34008 |
[24] |
Qian, D., Li, C., Agarwal, R.P., Wong, P.J.Y.: Stability analysis of fractional differential system with Riemann-Liouville derivative. Math. Comput. Model. 52, 862-874 (2010) · Zbl 1202.34020 · doi:10.1016/j.mcm.2010.05.016 |
[25] |
Sabatier, J., Moze, M., Farges, C.: LMI stability conditions for fractional order systems. Comput. Math. Appl. 59(5), 1594-1609 (2010) · Zbl 1189.34020 · doi:10.1016/j.camwa.2009.08.003 |
[26] |
Wang, J., Lv, L., Zhou, Y.: New concepts and results in stability of fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17(6), 2530-2538 (2012) · Zbl 1252.35276 · doi:10.1016/j.cnsns.2011.09.030 |
[27] |
Zhou, Y., Jiao, F.: Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 59(3), 1063-1077 (2010) · Zbl 1189.34154 · doi:10.1016/j.camwa.2009.06.026 |
[28] |
Zhang, H., Ye, R., Cao, J., Ahmed, A., Li, X., Ying, W.: Lyapunov functional approach to stability analysis of Riemann-Liouville fractional neural networks with time-varying delays. Asian J. Control 20(5), 1938-1951 (2018) · Zbl 1407.93348 · doi:10.1002/asjc.1675 |
[29] |
Altun, Y., Tunç, C.: On exponential stability of solutions of nonlinear neutral differential systems with discrete and distributed variable lags. Nonlinear Stud. 26(2), 455-466 (2019) · Zbl 1430.34080 |
[30] |
Balasubramaniam, P., Krishnasamy, R., Rakkiyappan, R.: Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach. Appl. Math. Model. 36, 2253-2261 (2012) · Zbl 1243.34105 · doi:10.1016/j.apm.2011.08.024 |
[31] |
Phat, V.N., Khongtham, Y., Ratchagit, K.: LMI approach to exponential stability of linear systems with interval time-varying delays. Linear Algebra Appl. 436, 243-251 (2012) · Zbl 1230.93076 · doi:10.1016/j.laa.2011.07.016 |
[32] |
Tunç, C., Altun, Y.: Asymptotic stability in neutral differential equations with multiple delays. J. Math. Anal. 7(5), 40-53 (2016) · Zbl 1362.34112 |
[33] |
Xiong, L., Zhong, S., Tian, J.: New robust stability condition for uncertain neutral systems with discrete and distributed delays. Chaos Solitons Fractals 42, 1073-1079 (2009) · Zbl 1198.93170 · doi:10.1016/j.chaos.2009.03.002 |
[34] |
Faieghi, M., Kuntanapreeda, S., Delavari, H., Baleanu, D.: LMI-based stabilization of a class of fractional-order chaotic systems. Nonlinear Dyn. 72(1-2), 301-309 (2013) · Zbl 1268.93121 · doi:10.1007/s11071-012-0714-6 |
[35] |
Faieghi, M., Mashhadi, S.K.M., Baleanu, D.: Sampled-data nonlinear observer design for chaos synchronization: a Lyapunov-based approach. Commun. Nonlinear Sci. Numer. Simul. 19(7), 2444-2453 (2014) · Zbl 1457.93023 · doi:10.1016/j.cnsns.2013.11.021 |
[36] |
Faieghi, M.R., Kuntanapreeda, S., Delavari, H., Baleanu, D.: Robust stabilization of fractional-order chaotic systems with linear controllers: LMI-based sufficient conditions. J. Vib. Control 20(7), 1042-1051 (2014) · doi:10.1177/1077546312475151 |
[37] |
Mobayen, S., Baleanu, D., Tchier, F.: Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems. J. Vib. Control 23(18), 2912-2925 (2017) · Zbl 1402.93134 · doi:10.1177/1077546315623887 |
[38] |
Wu, G.C., Baleanu, D., Luo, W.H.: Lyapunov functions for Riemann-Liouville-like fractional difference equations. Appl. Math. Comput. 314, 228-236 (2017) · Zbl 1426.39010 |
[39] |
Hajipour, M., Jajarmi, A., Baleanu, D.: On the accurate discretization of a highly nonlinear boundary value problem. Numer. Algorithms 79(3), 679-695 (2018) · Zbl 1405.65143 · doi:10.1007/s11075-017-0455-1 |
[40] |
Hajipour, M., Jajarmi, A., Malek, A., Baleanu, D.: Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation. Appl. Math. Comput. 325, 146-158 (2018) · Zbl 1429.65183 |