On Liapunov and the Stability Theory
Keywords:
Lyapunov stability theory, mathematics historyAbstract
In this work some ideas about the history of the stability concept from Lyapunov, its development until now and some open problems are presented.
Author Biographies
Miguel Vivas-Cortez, Pontificia Universidad Católica del Ecuador
Pontificia Universidad Cat\'olica del Ecuador (PUCE), \\ Facultad de Ciencias Exactas y Naturales,\\
Escuela de Ciencias Físicas y Matemática,
Sede Quito, Ecuador
Juan E. Napoles Valdés, Universidad Nacional Nordeste
UNNE, FaCENA Ave. Libertad 5450, Corrientes 3400, Argentina
UTN-FRRE, French 414, Resistencia, Chaco 3500, Argentina
References
[1] A. Fleitas, J. E. Na ́poles, J. M. Rodr ́ıguez, J. M. Sigarreta. On the generalized fractional derivative, Revista de la UMA, to appear.
[2] P.M.Guzma ́n,G.Langton,L.LugoMotta,J.Medina,J.E.Na ́polesV.,ANewdefinitionofafractional derivative of local type. J. Mathem. Anal. 9(2), pp. 88-98. 2018.
[3] P. M. Guzma ́n, L. Lugo Motta, J. E. Na ́poles V. On the stability of solutions of fractional non conformable differential equations. Stud. Univ. Babes-Bolyai Math. 65(2020), No. 4, 495-502 DOI: 10.24193/subbmath.2020.4.02
[4] P. M. Guzma ́n, L. Lugo Motta, J. E. Na ́poles V., A note on stability of certain Lienard fractional equation. International Journal of Mathematics and Computer Science, 14(2019), no. 2, 301-315.
[5] P. M. Guzma ́n, L. M. Lugo, J. E. Na ́poles Valde ́s, M. Vivas. On a New Generalized Integral Operator and Certain Operating Properties. Axioms 2020, 9, 69; doi:10.3390/axioms9020069.
[6] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math., 264, 65-70 (2014).
[7] F. Mart ́ınez, J. E. Na ́poles V., A note on the asymptotic properties of a generalized differential equa- tions. JFCA-2022/13(1), 30-41
[8] J. E. Na ́poles Valde ́s, On the continuability of solutions of bidimensional systems. Revista Extracta Mathematicae 11(1996), 366-368
[9] J. E. Na ́poles Valde ́s. El legado histo ́rico de las ecuaciones diferenciales ordinarias. Consideraciones (auto)cr ́ıticas, Bolet ́ın de Matema ́ticas, V(1998), 53-79
[10] J.E.Na ́polesValde ́s,Anoteontheasymptoticstabilityinthewholeofnonautonomoussystems.Revista Colombiana de Matema ́ticas 33(1999), 1-8
[11] J.E.Na ́polesValde ́s,Unsiglodeteor ́ıacualitativadeecuacionesdiferenciales.LecturasMatema ́ticas, Volumen 25 (2004), 59-111
[12] J. E. Na ́poles Valde ́s, Las ecuaciones diferenciales ordinarias como signos de los tiempos. Revista Eureka 21(2006), 39-75
[13] J. E. Na ́poles Valde ́s, Ecuaciones diferenciales y contemporaneidad. Revista Brasileira de Histo ́ria da Matema ́tica 7(14), 213-232, 2007
[14] J. E. Na ́poles, Generalized fractional Hilfer integral and derivative. Contrib. Math. 2 (2020) 55-60 DOI: 10.47443/cm.2020.0036
[15] J.E.Na ́polesV.,P.M.Guzma ́n,L.LugoMotta,SomeNewResultsontheNonConformableFractional Calculus. Advances in Dynamical Systems and Applications, Volume 13, Number 2, pp. 167?175 (2018).
[16] J. E. Na ́poles, P. M. Guzma ́n, L. M. Lugo, A. Kashuri. The local generalized derivative and Mittag Leffler function. Sigma Journal of Engineering and Natural Sciences, Sigma J Eng & Nat Sci 38 (2), 2020, 1007-1017
[17] D. Zhao and M. Luo. General conformable fractional derivative and its physical interpretation. Cal- colo, 54: 903-917, 2017. DOI 10.1007/s10092-017-0213-8.
[2] P.M.Guzma ́n,G.Langton,L.LugoMotta,J.Medina,J.E.Na ́polesV.,ANewdefinitionofafractional derivative of local type. J. Mathem. Anal. 9(2), pp. 88-98. 2018.
[3] P. M. Guzma ́n, L. Lugo Motta, J. E. Na ́poles V. On the stability of solutions of fractional non conformable differential equations. Stud. Univ. Babes-Bolyai Math. 65(2020), No. 4, 495-502 DOI: 10.24193/subbmath.2020.4.02
[4] P. M. Guzma ́n, L. Lugo Motta, J. E. Na ́poles V., A note on stability of certain Lienard fractional equation. International Journal of Mathematics and Computer Science, 14(2019), no. 2, 301-315.
[5] P. M. Guzma ́n, L. M. Lugo, J. E. Na ́poles Valde ́s, M. Vivas. On a New Generalized Integral Operator and Certain Operating Properties. Axioms 2020, 9, 69; doi:10.3390/axioms9020069.
[6] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math., 264, 65-70 (2014).
[7] F. Mart ́ınez, J. E. Na ́poles V., A note on the asymptotic properties of a generalized differential equa- tions. JFCA-2022/13(1), 30-41
[8] J. E. Na ́poles Valde ́s, On the continuability of solutions of bidimensional systems. Revista Extracta Mathematicae 11(1996), 366-368
[9] J. E. Na ́poles Valde ́s. El legado histo ́rico de las ecuaciones diferenciales ordinarias. Consideraciones (auto)cr ́ıticas, Bolet ́ın de Matema ́ticas, V(1998), 53-79
[10] J.E.Na ́polesValde ́s,Anoteontheasymptoticstabilityinthewholeofnonautonomoussystems.Revista Colombiana de Matema ́ticas 33(1999), 1-8
[11] J.E.Na ́polesValde ́s,Unsiglodeteor ́ıacualitativadeecuacionesdiferenciales.LecturasMatema ́ticas, Volumen 25 (2004), 59-111
[12] J. E. Na ́poles Valde ́s, Las ecuaciones diferenciales ordinarias como signos de los tiempos. Revista Eureka 21(2006), 39-75
[13] J. E. Na ́poles Valde ́s, Ecuaciones diferenciales y contemporaneidad. Revista Brasileira de Histo ́ria da Matema ́tica 7(14), 213-232, 2007
[14] J. E. Na ́poles, Generalized fractional Hilfer integral and derivative. Contrib. Math. 2 (2020) 55-60 DOI: 10.47443/cm.2020.0036
[15] J.E.Na ́polesV.,P.M.Guzma ́n,L.LugoMotta,SomeNewResultsontheNonConformableFractional Calculus. Advances in Dynamical Systems and Applications, Volume 13, Number 2, pp. 167?175 (2018).
[16] J. E. Na ́poles, P. M. Guzma ́n, L. M. Lugo, A. Kashuri. The local generalized derivative and Mittag Leffler function. Sigma Journal of Engineering and Natural Sciences, Sigma J Eng & Nat Sci 38 (2), 2020, 1007-1017
[17] D. Zhao and M. Luo. General conformable fractional derivative and its physical interpretation. Cal- colo, 54: 903-917, 2017. DOI 10.1007/s10092-017-0213-8.
How to Cite
Vivas-Cortez, M., & Napoles Valdés, J. E. . (2021). On Liapunov and the Stability Theory. Revista MATUA ISSN: 2389-7422, 8(1), 92–100. Retrieved from https://www.revistasuniatlanticoeduco.biteca.online/index.php/MATUA/article/view/3009
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Published
2021-08-19
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