
AIMS Mathematics, 2020, 5(4): 38093824. doi: 10.3934/math.2020247.
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Existence, continuous dependence and finite time stability for RiemannLiouville fractional differential equations with a constant delay
Department of Applied Mathematics and Modeling, University of Plovdiv “P. Hilendarski”, Plovdiv 4000, Bulgaria
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Keywords: RiemannLiouville fractional derivative; constant delay; initial value problem; existence; finite time stability
Citation: Snezhana Hristova, Antonia Dobreva. Existence, continuous dependence and finite time stability for RiemannLiouville fractional differential equations with a constant delay. AIMS Mathematics, 2020, 5(4): 38093824. doi: 10.3934/math.2020247
References:
 1. H. Zhang, R. Ye, S. Liu, et al. LMIbased approach to stability analysis for fractionalorder neural networks with discrete and distributed delays, Int. J. Syst. Sci., 49 (2018), 537545.
 2. W. Zhang, J. Cao, R. Wu, et al. Lag projective synchronization of fractionalorder delayed chaotic systems, J. Franklin Institute, 356 (2019), 15221534.
 3. W. Zhang, H. Zhang, J. Cao, et al. Synchronization in uncertain fractionalorder memristive complexvalued neural networks with multiple time delays, Neural Networks, 110 (2019), 186198.
 4. P. Dorato, Short time stability in linear timevarying systems, Proc. IRE Int. Convention Record, 4 (1961), 8387.
 5. D. F. Luo, Z. G. Luo, Uniqueness and novel finitetime stability of solutions for a class of nonlinear fractional delay difference systems, Discr. Dynam, Nature Soc., 2018 (2018), 17.
 6. G. C. Wu, D. Baleanu, S. D. Zeng, Finitetime stability of discrete fractional delay systems: Gronwall inequality and stability criterion, Commun. Nonl. Sci. Numer. Simul., 57 (2018), 299308.
 7. V. N. Phat, N. T. Thanh, New criteria for finitetime stability of nonlinear fractionalorder delay systems: A Gronwall inequality approach, Appl. Math. Lett., 83 (2018), 169175.
 8. D. F. Luo, Z. G. Luo, Existence and finitetime stability of solutions for a class of nonlinear fractional differential equations with timevarying delays and noninstantaneous impulses, Adv. Diff. Eq., 155, 2019.
 9. D. Qian, C. Li, R. P. Agarwal, et al. Stability analysis of fractional differential system with RiemannLiouville derivative, Math. Comput. Modell., 52 (2010), 862874.
 10. M. Li, J. Wang, Finite time stability of fractional delay differential equations, Appl. Math. Lett., 64 (2017), 170176.
 11. M. Li, J. R. Wang, Exploring delayed MittagLeffler type matrix functions to study finite time stability of fractional delay differential equations, Appl. Math. Comput., 324 (2018), 254265.
 12. M. Li, J. R. Wang, Finite time stability and relative controllability of RiemannLiouville fractional delay differential equations, Math. Meth. Appl. Sci., 2019 (2019), 117.
 13. K. Diethelm, The Analysis of Fractional Differential Equations, SpringerVerlag, Berlin, Heidelberg, 2010.
 14. I. Podlubny, Fractional Differential Equations, Academic Press: San Diego, 1999.
 15. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
 16. H. Ye, J. Gao, Y. Ding, A generalized Gronwall inequality and its application to a fracnal differential equation, J. Math. Anal. Appl., 328 (2007), 10751081.
 17. R. Agarwal, S. Hristova, D. O'Regan, Explicit solutions of initial value problems for linear scalar RiemannLiouville fractional differential equations with a constant delay, Mathematics, 8 (2020), 114.
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