On the stability of solutions of fractional non conformable differential equations
DOI:
https://doi.org/10.24193/subbmath.2020.4.02Keywords:
fractional non conformable system of equations, Lyapunov Seond Method, stability, asymptotic stability, instabilityAbstract
In this note we obtain sucient conditions under which we can guarantee the stability of solutions of a fractional differential equations of non
conformable type and we obtain some fractional analogous theorems of
the direct Lyapunov method for a given class of equations of motion.
References
Abdeljawad, T. (2015). On conformable fractional calculus. J. Comput.
Appl. Math., 279, pp. 57-66.
P. M. Guzman, Guillermo Langton, L. Lugo Motta, Julian Medina, and J. E. Napoles V., A New definition of a fractional derivative of local type, J.
Mathem. Anal. 9(2) (2018), 88-98.
P. M. Guzman, L. Lugo Motta, and J. E. Napoles V., A note on stability of certain Lienard fractional equation, International Journal of Mathematics and Computer Science, 14(2019), no. 2, to appear.
Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M. (2014). A new
denition of fractional derivative. J. Comput. Appl. Math., 264, pp. 65-70.
Kilbas, A., Srivastava, M.H. and Trujillo, J. J. (2006). Theory and application on fractional differential equations. Amsterdam: North Holland.
Lakshmikantham, V., Leela, S. and Devi, J. V. (2009). Theory of fractional dynamic systems. Cambridge: Cambridge Scientic Publ.
Lienard, A.-Etude des oscillations entretenues, Revue Generale de
l'Electricite 23: 901-912, 946-954 (1928).
Lyapunov, A. M. (1935). The general problem of motion stability.
Leningrad, Moscow: ONTI (in Russian).
Martynyuk, A. A. (2016). On the stability of a system of equations with fractional derivatives with respect to two measures. J. Math. Sci., 217, No. 4, pp. 468-475.
Martynyuk, A. A. (2018). Lyapunov direct method, stability, asymptotic stability, instability, Dopov. Nac. akad. nauk Ukr. 2018, No. 6, 9-16.
Napoles V., Juan E.-"A note on the asymptotic stability in the whole of nonautonomous systems", Revista Colombiana de Matematicas, 33(1999), 1-8.
J. E. Napoles V., P. M. Guzman, and L. Lugo Motta, Some New Results on the Non Conformable Fractional Calculus, Advances in Dynamical Systems and Applications, Volume 13, Number 2, pp. 167{175 (2018).
Podlybny, I. (1999). Fractional differential equations. London, Acad. Press.
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