Browse > Article
http://dx.doi.org/10.4134/BKMS.b180749

MITTAG-LEFFLER STABILITY OF SYSTEMS OF FRACTIONAL NABLA DIFFERENCE EQUATIONS  

Eloe, Paul (Department of Mathematics University of Dayton)
Jonnalagadda, Jaganmohan (Department of Mathematics Birla Institute of Technology and Science Pilani)
Publication Information
Bulletin of the Korean Mathematical Society / v.56, no.4, 2019 , pp. 977-992 More about this Journal
Abstract
Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.
Keywords
fractional order nabla difference; discrete Mittag-Leffler function; discrete exponential function; N-transform; Mittag-Leffler stability;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 D. D. Anderson and T. Dumitrescu, S-Noetherian rings, Comm. Algebra 30 (2002), no. 9, 4407-4416. https://doi.org/10.1081/AGB-120013328   DOI
2 L. Angeleri Hugel and D. Herbera, Mittag-Leffler conditions on modules, Indiana Univ. Math. J. 57 (2008), no. 5, 2459-2517. https://doi.org/10.1512/iumj.2008.57.3325   DOI
3 G. Azumaya, Finite splitness and finite projectivity, J. Algebra 106 (1987), no. 1, 114-134. https://doi.org/10.1016/0021-8693(87)90024-X   DOI
4 J. Baeck, G. Lee, and J. W. Lim, S-Noetherian rings and their extensions, Taiwanese J. Math. 20 (2016), no. 6, 1231-1250. https://doi.org/10.11650/tjm.20.2016.7436   DOI
5 S. Bazzoni and L. Positselski, S-almost perfect commutative rings, eprint arXiv:1801.04820, (2018).
6 D. Bennis and M. El Hajoui, On S-coherence, J. Korean Math. Soc. 55 (2018), no. 6, 1499-1512.   DOI
7 M. Cortes-Izurdiaga, Products of flat modules and global dimension relative to F-Mittag-Leffler modules, Proc. Amer. Math. Soc. 144 (2016), no. 11, 4557-4571. https://doi.org/10.1090/proc/13059   DOI
8 F. Couchot, Finitistic weak dimension of commutative arithmetical rings, Arab. J. Math. (Springer) 1 (2012), no. 1, 63-67. https://doi.org/10.1007/s40065-012-0023-4   DOI
9 K. R. Goodearl, Distributing tensor product over direct product, Pacific J. Math. 43 (1972), 107-110. http://projecteuclid.org/euclid.pjm/1102959646   DOI
10 P. Griffth, On the decomposition of modules and generalized left uniserial rings, Math. Ann. 184 (1969/1970), 300-308. https://doi.org/10.1007/BF01350858   DOI
11 D. Herbera and J. Trlifaj, Almost free modules and Mittag-Leffler conditions, Adv. Math. 229 (2012), no. 6, 3436-3467. https://doi.org/10.1016/j.aim.2012.02.013   DOI
12 H. Kim, M. O. Kim, and J. W. Lim, On S-strong Mori domains, J. Algebra 416 (2014), 314-332. https://doi.org/10.1016/j.jalgebra.2014.06.015   DOI
13 H. Kim and J. W. Lim, $S-\ast_w$-principal ideal domains, Algebra Colloq. 25 (2018), no. 2, 217-224. https://doi.org/10.1142/S1005386718000159   DOI
14 J. W. Lim, A note on S-Noetherian domains, Kyungpook Math. J. 55 (2015), no. 3, 507-514. https://doi.org/10.5666/KMJ.2015.55.3.507   DOI
15 J. J. Rotman, An Introduction to Homological Algebra, second edition, Universitext, Springer, New York, 2009. https://doi.org/10.1007/b98977
16 S. U. Chase, Direct products of modules, Trans. Amer. Math. Soc. 97 (1960), 457-473. https://doi.org/10.2307/1993382   DOI
17 J. W. Lim and D. Y. Oh, S-Noetherian properties on amalgamated algebras along an ideal, J. Pure Appl. Algebra 218 (2014), no. 6, 1075-1080. https://doi.org/10.1016/j.jpaa.2013.11.003   DOI
18 J. W. Lim and D. Y. Oh, S-Noetherian properties of composite ring extensions, Comm. Algebra 43 (2015), no. 7, 2820-2829. https://doi.org/10.1080/00927872.2014.904329   DOI
19 Ph. Rothmaler, Mittag-Leffler modules and positive atomicity, Habilitationsschrift, Kiel, 1994.
20 Ph. Rothmaler, Torsion-free, divisible, and Mittag-Leffler modules, Comm. Algebra 43 (2015), no. 8, 3342-3364. https://doi.org/10.1080/00927872.2014.918990   DOI
21 D. Simson, On pure global dimension of locally finitely presented Grothendieck categories, Fund. Math. 96 (1977), no. 2, 91-116. https://doi.org/10.4064/fm-96-2-91-116   DOI