[1] |
Zhou, Y.; Wang, J. R.; Zhang, L., Basic theory of fractional differential equations (2014), World Scientific: World Scientific Singapore · Zbl 1336.34001 |
[2] |
Kilbas, A. A.; Srivastava, H. M.; Trujillo, J. J., Theory and applications of fractional differential equations (2006), Elsevier: Elsevier Amsterdam · Zbl 1092.45003 |
[3] |
Podlubny, I.; Thimann, K. V., Fractional differential equation (1999), Academic Press: Academic Press San Diego · Zbl 0924.34008 |
[4] |
Miller, K. S.; Ross, B., An introduction to the fractional calculus and fractional differential equations (1993), Wiley: Wiley New York · Zbl 0789.26002 |
[5] |
Diethelm, K., The analysis of fractional differential equations (2010), Springer: Springer New York · Zbl 1215.34001 |
[6] |
Mao, X. R., Stochastic differential equations and applications (2011), Woodhead Publishing Limited: Woodhead Publishing Limited Abington Hall |
[7] |
Prato, G. D.; Zabczyk, J., Stochastic equations in infinite dimensions (1992), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0761.60052 |
[8] |
Øksendal, B., Stochastic differential equations, an introduction with applications (2003), Springer-Verlag: Springer-Verlag Heidelberg · Zbl 1025.60026 |
[9] |
Evans, L. C., An introduction to stochastic differential equations (2014), American Mathematical Society: American Mathematical Society Providence |
[10] |
Benchohra, M.; Henderson, J.; Ntouyas, S. K., Impulsive differential equations and inclusions (2006), Hindawi Publishing Corporation: Hindawi Publishing Corporation New York · Zbl 1130.34003 |
[11] |
Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of impulsive differential equations (1989), World Scientific: World Scientific Singapore, London · Zbl 0719.34002 |
[12] |
Haddad, W. M.; Chellaboina, V.; Nersesov, S. G., Impulsive and hybrid dynamical systems (2006), Princeton University Press: Princeton University Press Princeton · Zbl 1114.34001 |
[13] |
Atay, F. M., Complex time-delay systems (2010), Springer: Springer Berlin Heidelberg · Zbl 1189.93005 |
[14] |
Gorenflo, R.; Kilbas, A. A.; Mainardi, F.; Rogosin, S. V., Mittag-leffler functions, related topics and applications (2014), Springer-Verlag: Springer-Verlag Berlin · Zbl 1309.33001 |
[15] |
Ye, H. P.; Gao, J. M., Henry-gronwall type retarded integral inequalities and their applications to fractional differential equations with delay, Appl Math Comput, 218, 8, 4152-4160 (2011) · Zbl 1247.26043 |
[16] |
Luo, D. F.; Zhu, Q. X.; Luo, Z. G., An averaging principle for stochastic fractional differential equations with time-delays, Appl Math Lett, 105, Article 106290 pp. (2020) · Zbl 1436.34072 |
[17] |
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, 7, 3050-3060 (2012) · Zbl 1252.35277 |
[18] |
Yan, Z. M.; Jia, X. M., Existence of optimal mild solutions and controllability of fractional impulsive stochastic partial integro-differential equations with infinite delay, Asian J Control, 21, 3, 725-748 (2019) · Zbl 1422.93020 |
[19] |
Yan, Z. M.; Jia, X. M., Optimal solutions of fractional nonlinear impulsive neutral stochastic functional integro-differential equations, Numer Funct Anal Optim, 40, 14, 1593-1643 (2019) · Zbl 1425.34092 |
[20] |
Ma, X.; Shu, X. B.; Mao, J. Z., Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay, Stoch Dyn, 20, 1, Article 2050003 pp. (2020) · Zbl 1442.34125 |
[21] |
Deng, S. F.; Shu, X. B.; Mao, J. Z., Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Mönch fixed point, J Math Anal Appl, 467, 1, 398-420 (2018) · Zbl 1405.60075 |
[22] |
Shu, X. B.; Lai, Y. Z.; Chen, Y. M., The existence of mild solutions for impulsive fractional partial differential equations, Nonlinear Anal, 74, 5, 2003-2011 (2011) · Zbl 1227.34009 |
[23] |
Arthi, G.; Park, J. H.; Jung, H. Y., Existence and exponential stability for neutral stochastic integrodifferential equations with impulses driven by a fractional brownian motion, Commun Nonlinear Sci Numer Simul, 32, 145-157 (2016) · Zbl 1510.60045 |
[24] |
Liu, J. K.; Xu, W.; Guo, Q., Global attractiveness and exponential stability for impulsive fractional neutral stochastic evolution equations driven by fBm, Adv Difference Equ, 2020, 1, 63 (2020) · Zbl 1487.34155 |
[25] |
Abouagwa, M.; Cheng, F. F.; Li, J., Impulsive stochastic fractional differential equations driven by fractional brownian motion, Adv Difference Equ, 2020, 1, 57 (2020) · Zbl 1487.60104 |
[26] |
Abouagwa, M.; Li, J., Approximation properties for solutions to Itô doob stochastic fractional differential equations with non-lipschitz coefficients, Stoch Dyn, 19, 4, Article 1950029 pp. (2019) · Zbl 1422.34011 |
[27] |
Abouagwa, M.; Liu, J. C.; Li, J., Carathéodory approximations and stability of solutions to non-lipschitz stochastic fractional differential equations of Itô-doob type, Appl Math Comput, 329, 143-153 (2018) · Zbl 1427.34079 |
[28] |
Moghaddam, B. P.; Zhang, L.; Lopes, A. M.; Tenreiro Machado, J. A.; Mostaghim, Z. S., Sufficient conditions for existence and uniqueness of fractional stochastic delay differential equations, Stochastics, 92, 3, 379-396 (2019) · Zbl 1490.60172 |
[29] |
Umamaheswari, P.; Balachandran, K.; Annapoorani, N., Existence and stability results for caputo fractional stochastic differential equations with Lévy noise, Filomat, 34, 5, 1739-1751 (2020) · Zbl 1529.60041 |
[30] |
Ahmadova, A.; Mahmudov, N. I., Existence and uniqueness results for a class of fractional stochastic neutral differential equations, Chaos Solitons Fractals, 139, Article 110253 pp. (2020) · Zbl 1490.34094 |
[31] |
Anh, P. T.; Doan, T. S.; Huong, P. T., A variation of constant formula for caputo fractional stochastic differential equations, Statist Probab Lett, 145, 351-358 (2019) · Zbl 1410.34013 |
[32] |
Li, K. X.; Peng, J. G., Laplace transform and fractional differential equations, Appl Math Lett, 24, 12, 2019-2023 (2011) · Zbl 1238.34013 |
[33] |
Luo, D. F.; Zhu, Q. X.; Luo, Z. G., A novel result on averaging principle of stochastic hilfer-type fractional system involving non-lipschitz coefficients, Appl Math Lett, 122, Article 107549 pp. (2021) · Zbl 1481.60114 |
[34] |
Nadeem, M.; Dabas, J., Solvability of fractional order semi-linear stochastic impulsive differential equation with state-dependent delay, Proc Natl Acad Sci, India, Sect A Phys Sci, 90, 3, 411-419 (2020) · Zbl 1458.34135 |
[35] |
Lazarević, M. P.; Spasić, A. M., Finite-time stability analysis of fractional order time-delay systems: Gronwall’s approach, Math Comput Model, 49, 3-4, 475-481 (2009) · Zbl 1165.34408 |
[36] |
Zhang, Y. R.; Wang, J. R., Existence and finite-time stability results for impulsive fractional differential equations with maxima, J Appl Math Comput, 51, 67-79 (2016) · Zbl 1346.34053 |
[37] |
Luo, Z. J.; Wang, J. R., Finite time stability analysis of systems based on delayed exponential matrix, J Appl Math Comput, 55, 335-351 (2017) · Zbl 1378.34090 |
[38] |
Li, M. M.; Wang, J. R., Finite time stability of fractional delay differential equations, Appl Math Lett, 64, 170-176 (2017) · Zbl 1354.34130 |
[39] |
Li, M. M.; Wang, J. R., Exploring delayed mittag-leffler type matrix functions to study finite time stability of fractional delay differential equations, Appl Math Comput, 324, 254-265 (2018) · Zbl 1426.34110 |
[40] |
Li, M. M.; Wang, J. R., Finite time stability and relative controllability of riemann-liouville fractional delay differential equations, Math Methods Appl Sci, 42, 18, 5945-7545 (2019) · Zbl 1440.34082 |
[41] |
Luo, Z. J.; Wei, W.; Wang, J. R., Finite time stability of semilinear delay differential equations, Nonlinear Dyn, 89, 713-722 (2017) · Zbl 1374.34285 |
[42] |
You, Z. L.; Wang, J. R.; Zhou, Y.; Fečkan, M., Representation of solutions and finite time stability for delay differential systems with impulsive effects, Int J Nonlinear Sci Numer Simul, 20, 2, 205-221 (2019) · Zbl 07048619 |
[43] |
Wang, J. R.; Luo, Z. J., Finite time stability of semilinear multi-delay differential systems, Trans Inst Meas Control, 40, 9, 2948-2959 (2017) |
[44] |
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 |
[45] |
Du, F. F.; Lu, J. G., Finite-time stability of neutral fractional order time delay systems with lipschitz nonlinearities, Appl Math Comput, 375, Article 125079 pp. (2020) |
[46] |
Du, F. F.; Lu, J. G., New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay, Appl Math Comput, 389, Article 125616 pp. (2021) · Zbl 1508.34058 |
[47] |
Du, F. 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, 32, 9, 3858-3866 (2021) |
[48] |
Du, F. F.; Lu, J. G., Finite-time stability of fractional-order fuzzy cellular neural networks with time delays, Fuzzy Set Syst (2021) |
[49] |
Luo, D. F.; Luo, Z. G., Uniqueness and novel finite-time stability of solutions for a class of nonlinear fractional delay difference systems, Discrete Dyn Nat Soc, 2018, 8476285 (2018) · Zbl 1417.39060 |
[50] |
Luo, D. F.; Luo, Z. G., Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses, Adv Difference Equ, 2019, 155 (2019) · Zbl 1459.34032 |
[51] |
Li, Q.; Luo, D. F.; Luo, Z. G.; Zhu, Q. X., On the novel finite-time stability results for uncertain fractional delay differential equations involving noninstantaneous impulses, Math Probl Eng, 2019, 9097135 (2019) · Zbl 1435.93140 |