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 second method, stability, asymptotic stability, instability.Abstract
In this note we obtain sufficient 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.
Mathematics Subject Classification (2010): 34A08.
References
Abdeljawad, T., On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279(2015), 57-66.
Guzma´n, P.M., Langton, G., Lugo Motta, L., Medina, J., N´apoles V., J.E., A New definition of a fractional derivative of local type, J. Mathem. Anal., 9(2018), no. 2, 88- 98.
Guzma´n, P.M., Lugo Motta, L., N´apoles V., J.E., A note on stability of certain Lienard fractional equation, International Journal of Mathematics and Computer Science, 14(2019), no. 2, 301-315.
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative, Journal of Computational and Applied Mathematics, 264, 65-70.
Kilbas, A., Srivastava, M.H., Trujillo, J.J., Theory and Application on Fractional Differential Equations, vol. 204, North-Holland Mathematics Studies, 2006.
Lakshmikantham, V., Leela, S., Devi, J.V., Theory of Fractional Dynamic Systems, Cambridge: Cambridge Scientific Publ., 2009.
Li´enard, A., E´tude des oscillations entretenues, Revue G´enerale de l’E´ lectricit´e, 23 (1928), 901-912, 946-954.
Lyapunov, A.M., The General Problem of Motion Stability, (in Russian), Leningrad, Moscow: ONTI, 1935.
Martynyuk, A.A., On the stability of a system of equations with fractional derivatives with respect to two measures, Journal of Mathematical Sciences, 217(2016), no. 4, 468- 475.
Martynyuk, A.A., Lyapunov direct method, stability, asymptotic stability, instability, Dopov. Nats. Akad. Nauk Ukr., (2018), no. 6, 9-16.
N´apoles V., J.E., A note on the asymptotic stability in the whole of nonautonomous systems, Revista Colombiana de Matem´aticas, 33(1999), 1-8.
N´apoles V., J.E., Guzman, P.M., Lugo Motta, L., Some new results on the non conformable fractional calculus, Advances in Dynamical Systems and Applications, 13(2018), no. 2, 167-175.
Podlybny, I., Fractional Differential Equations, London, Acad. Press, 1999.
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