Fractional-like Hukuhara derivative and its properties

1Martynyuk, AA
1S.P. Timoshenko Institute of Mechanics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 4:10-16
https://doi.org/10.15407/dopovidi2019.04.010
Section: Mathematics
Language: Russian
Abstract: 

The concept of fractional-like Hukuhara derivative for set-valued maps is introduced, its properties are discussed, and the principle of comparison is established for fractional-like set-valued differential equations.

Keywords: fraction-like Hukuhara derivative, set-valued of fractional-like differential equations, the principle of comparison
References: 

1. Hukuhara, M. (1967). Sur l′application semi-continue dont la valeur est un compact convexe. Funkcial. Ekvac., 10, pp. 43-66.
2. Burton, T. A. (2012). Lyapunov theory for integral equations with singular kernels and fractional differential equations. Port Angeles, WA.
3. Kilbas, A., Srivastava, M. H. & Trujillo, J. J. (2006). Theory and application on fractional differential equations. Amsterdam: North Holland.
4. Lakshmikantham, V., Leela, S. & Devi, J. V. (2009).Theory of fractional dynamic systems. Cambridge: Cambridge Scientific Publ.
5. Podlybny, I. (1999). Fractional differential equations. London: Academic Press.
6. Martynyuk, A. A., Stamova, I. & Martynyuk-Chernienko, Yu. A. (2017). Stability analysis of set of trajectories for differential equations with fractional dynamics. Eur. Phys. J. Special Topics, 226, pp. 3609-3637. doi: https://doi.org/10.1140/epjst/e2018-00051-7
7. Khalil, R., Al Horani, M., Yousef, A. & Sababheh, M. (2014). A new definition of fractional derivative. J. Comput. Appl. Math., 264, pp. 65-70. doi: https://doi.org/10.1016/j.cam.2014.01.002
8. Abdeljawad, T. (2015). On conformable fractional calculus. J. Comput. Appl. Math., 279, pp. 57-66. doi: https://doi.org/10.1016/j.cam.2014.10.016
9. Martynyuk, A. А. (2018).On stability analysis of fractional-like systems of perturbed motion. Dopov. Nac. akad. nauk Ukr., No. 6, pp. 9-16 (in Russian). doi: https://doi.org/10.15407/dopovidi2018.06.009
10. Martynyuk, A. A. & Stamova, I. M. (2018). Fractional-like derivative of Lyapunov-type functions and applications to the stability analysis of motion. Electron. J. Differential Equations, 2018, No. 62, pp. 1-12.
11. Martynyuk, A. A., Stamov, G. & Stamova, I. M. (2019). Integral estimates of the solutions of fractional-like equations of perturbed motion. Nonlinear Analysis: Modelling and Control, 24, No. 1, pp. 138-149. doi: https://doi.org/10.15388/NA.2019.1.8