[1] |
Abbas, S.; Benchohra, M.; N’Gurkata, G. M., Topics in Fractional Differential Equations (2012), Berlin: Springer, Berlin · Zbl 1273.35001 · doi:10.1007/978-1-4614-4036-9 |
[2] |
Baleanu, D.; Diethelm, K.; Scalas, E.; Trujillo, J. J., Fractional Calculus Models and Numerical Methods (2012), Singapore: World Scientific, Singapore · Zbl 1248.26011 · doi:10.1142/8180 |
[3] |
Chen, C.; Jia, B.; Liu, X.; Erbe, L., Existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay, Mediterr. J. Math., 15 (2018) · Zbl 1403.39003 · doi:10.1007/s00009-018-1258-x |
[4] |
Chen, L.; Hao, Y.; Huang, T.; Yuan, L.; Zheng, S.; Yin, L., Chaos in fractional-order discrete neural networks with application to image encryption, Neural Netw., 125, 174-184 (2020) · doi:10.1016/j.neunet.2020.02.008 |
[5] |
Chen, L.; Wu, R.; He, Y.; Yin, L., Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties, Appl. Math. Comput., 257, 274-284 (2015) · Zbl 1338.93293 |
[6] |
Deng, W.; Li, C.; Lü, J., Stability analysis of linear fractional differential system with multiple time delays, Nonlinear Dyn., 48, 409-416 (2007) · Zbl 1185.34115 · doi:10.1007/s11071-006-9094-0 |
[7] |
Dragomir, S. S., Some Gronwall Type Inequalities and Applications (2003), New York: Nova Science, New York · Zbl 1094.34001 |
[8] |
Du, F.; Jia, B., Finite-time stability of a class of nonlinear fractional delay difference systems, Appl. Math. Lett., 98, 233-239 (2019) · Zbl 1473.39026 · doi:10.1016/j.aml.2019.06.017 |
[9] |
Du, F.; Jia, B., Finite-time stability of nonlinear fractional order systems with a constant delay, J. Nonlinear Model. Anal., 2, 1-13 (2020) |
[10] |
Du, F.; Lu, J. G., Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities, Appl. Math. Comput., 375 (2020) |
[11] |
Du, F., Lu, J.G.: New criteria on finite-time stability of fractional-order hopfield neural networks with time delays. IEEE Trans. Neural Netw. Learn. Syst. (2020) |
[12] |
Du, F.; Lu, J. G., New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay, Appl. Math. Comput., 389 (2021) · Zbl 1508.34058 |
[13] |
Gorenflo, R.; Mainardi, F.; Srivastava, H. M.; Bainov, D., Special functions in fractional relaxation-oscillation and fractional diffusion-wave phenomena, Proc. VIII International Colloquium on Differential Equations, Plovdiv 1997, 195-202 (1998), Utrecht: VSP (International Science Publishers), Utrecht · Zbl 0921.33009 |
[14] |
Hei, X.; Wu, R., Finite-time stability of impulsive fractional-order systems with time-delay, Appl. Math. Model., 40, 4285-4290 (2016) · Zbl 1459.34020 · doi:10.1016/j.apm.2015.11.012 |
[15] |
Huang, H.; Fu, X., Approximate controllability of semi-linear stochastic integro-differential equations with infinite delay, IMA J. Math. Control Inf., 37, 1133-1167 (2020) · Zbl 1514.93029 · doi:10.1093/imamci/dnz040 |
[16] |
Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations (2006), Amsterdam: Elsevier, Amsterdam · Zbl 1092.45003 |
[17] |
Lazarevic, M. P.; Spasic, A. M., Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach, Math. Comput. Model., 49, 475-481 (2009) · Zbl 1165.34408 · doi:10.1016/j.mcm.2008.09.011 |
[18] |
Li, M.; Wang, J., Finite time stability of fractional delay differential equations, Appl. Math. Lett., 64, 170-176 (2017) · Zbl 1354.34130 · doi:10.1016/j.aml.2016.09.004 |
[19] |
Li, P.; Chen, L.; Wu, R.; Machado, J. T.; Lopes, A. M.; Yuan, L., Robust asymptotic stability of interval fractional-order nonlinear systems with time-delay, J. Franklin Inst., 355, 7749-7763 (2018) · Zbl 1398.93281 · doi:10.1016/j.jfranklin.2018.08.017 |
[20] |
Li, Y.; Chen, Y.; Podlubny, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica, 45, 1965-1969 (2009) · Zbl 1185.93062 · doi:10.1016/j.automatica.2009.04.003 |
[21] |
Liang, C.; Wei, W.; Wang, J., Stability of delay differential equations via delayed matrix sine and cosine of polynomial degrees, Adv. Differ. Equ., 2017 (2017) · Zbl 1422.34209 · doi:10.1186/s13662-017-1188-0 |
[22] |
Liu, L.; Zhong, S., Finite-time stability analysis of fractional-order with multistate time delay, Int. J. Math. Comput. Sci., 5, 641-644 (2011) |
[23] |
Ma, Y. J.; Wu, B. W.; Wang, Y. E., Finite-time stability and finite-time boundedness of fractional order linear systems, Neurocomputing, 173, 2076-2082 (2016) · doi:10.1016/j.neucom.2015.09.080 |
[24] |
Ma, Y. K.; Arthi, G.; Marshal Anthoni, S., Exponential stability behavior of neutral stochastic integrodifferential equations with fractional Brownian motion and impulsive effects, Adv. Differ. Equ., 2018 (2018) · Zbl 1445.60034 · doi:10.1186/s13662-018-1562-6 |
[25] |
Mathiyalagan, K.; Balachandran, K., Finite-time stability of fractional-order stochastic singular systems with time delay and white noise, Complexity, 21, S2, 370-379 (2016) · doi:10.1002/cplx.21815 |
[26] |
Mathiyalagan, K.; Sangeetha, G., Second-order sliding mode control for nonlinear fractional-order systems, Appl. Math. Comput., 383 (2020) · Zbl 1508.93054 |
[27] |
Naifar, O.; Nagy, A. M.; Makhlouf, A. B.; Kharrat, M.; Hammami, M. A., Finite-time stability of linear fractional-order time-delay systems, Int. J. Robust Nonlinear Control, 29, 180-187 (2019) · Zbl 1411.93135 · doi:10.1002/rnc.4388 |
[28] |
Narahari Achar, B. N.; Hanneken, J. W.; Clarke, T., Response characteristics of a fractional oscillator, Phys. A, Stat. Mech. Appl., 309, 275-288 (2002) · Zbl 0995.70017 · doi:10.1016/S0378-4371(02)00609-X |
[29] |
Ngoc, P. H.A., Stability of periodic solutions of nonlinear time-delay systems, IMA J. Math. Control Inf., 34, 905-918 (2017) · Zbl 1417.93267 |
[30] |
Phat, V. N.; Thanh, N. T., New criteria for finite-time stability of nonlinear fractional-order delay systems: a Gronwall inequality approach, Appl. Math. Lett., 83, 169-175 (2018) · Zbl 1388.93064 · doi:10.1016/j.aml.2018.03.023 |
[31] |
Podlubny, I., Fractional Differential Equations (1998), New York: Academic Press, New York · Zbl 0922.45001 |
[32] |
Puangmalai, J.; Tongkum, J.; Rojsiraphisal, T., Finite-time stability criteria of linear system with non-differentiable time-varying delay via new integral inequality, Math. Comput. Simul., 171, 170-186 (2020) · Zbl 1510.93276 · doi:10.1016/j.matcom.2019.06.013 |
[33] |
Sheng, J.; Jiang, W., Existence and uniqueness of the solution of fractional damped dynamical systems, Adv. Differ. Equ., 2017 (2017) · Zbl 1422.34061 · doi:10.1186/s13662-016-1049-2 |
[34] |
Thanh, N. T.; Phat, V. N.; Niamsup, P., New finite-time stability analysis of singular fractional differential equations with time-varying delay, Fract. Calc. Appl. Anal., 23, 504-519 (2020) · Zbl 1453.34102 · doi:10.1515/fca-2020-0024 |
[35] |
Tuan, H. T.; Siegmund, S., Stability of scalar nonlinear fractional differential equations with linearly dominated delay, Fract. Calc. Appl. Anal., 23, 250-267 (2020) · Zbl 1441.34084 · doi:10.1515/fca-2020-0010 |
[36] |
Wu, G. C.; Baleanu, D.; Zeng, S. D., Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion, Commun. Nonlinear Sci. Numer. Simul., 57, 299-308 (2018) · Zbl 1510.39014 · doi:10.1016/j.cnsns.2017.09.001 |
[37] |
Xu, K.; Chen, L.; Wang, M.; Lopes, A. M.; Tenreiro Machado, J. A.; Zhai, H., Improved decentralized fractional PD control of structure vibrations, Mathematics, 8 (2020) · doi:10.3390/math8030326 |
[38] |
Ye, H.; Gao, J.; Ding, Y., A generalized Gronwall inequality and its application to a fractional differential equation, J. Math. Anal. Appl., 328, 1075-1081 (2007) · Zbl 1120.26003 · doi:10.1016/j.jmaa.2006.05.061 |
[39] |
Yonggang, K.; Xiu’e, Z., Some comparison of two fractional oscillator, Physica B, Condens. Matter, 405, 369-373 (2010) · doi:10.1016/j.physb.2009.08.092 |
[40] |
You, Z.; Wang, J., On the exponential stability of nonlinear delay systems with impulses, IMA J. Math. Control Inf., 35, 773-803 (2018) · Zbl 1402.93217 · doi:10.1093/imamci/dnw077 |
[41] |
Yu, J.; Hu, H.; Zhou, S.; Lin, X., Generalized Mittag-Leffler stability of multi-variables fractional order nonlinear systems, Automatica, 49, 1798-1803 (2013) · Zbl 1360.93513 · doi:10.1016/j.automatica.2013.02.041 |
[42] |
Zhang, C.; Niu, Y., The stability relation between ordinary and delay-integro-differential equations, Math. Comput. Model., 49, 13-19 (2009) · Zbl 1173.34044 · doi:10.1016/j.mcm.2008.07.036 |
[43] |
Zhang, F.; Qian, D.; Li, C., Finite-time stability analysis of fractional differential systems with variable coefficients, Chaos, 29 (2019) · Zbl 1406.34026 |
[44] |
Zhang, R.; Tian, G.; Yang, S.; Cao, H., Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2), ISA Trans., 56, 102-110 (2015) · doi:10.1016/j.isatra.2014.12.006 |