Fractional-like Hukuhara derivatives in the theory of set-valued differential equations
作者： Anatoliy A. Martynyuk , Gani Tr. Stamov , Ivanka M. Stamova
DOI: 10.1016/J.CHAOS.2019.109487
关键词:
摘要: Abstract In this paper a fractional-like Hukuhara-type derivative is introduced for set of equations. Connections between the new defined notion and classical Hukuhara are established and, in addition, some applications to theory set-valued differential equations discussed. Namely, family with derivatives states: (a) version comparison principle proposed; (b) local existence conditions derived; (c) an estimate deviation approximate solution from exact one given. With research we extend case.
sci-hub.se 参考文章(24)
V. Lakshmikantham, J. Vasundhara Devi, S. Leela, Theory of Fractional Dynamic Systems ,(2009)
Hari M Srivastava, Anatoly A Kilbas, Juan J Trujillo, Theory and Applications of Fractional Differential Equations ,(2006)
Ivanka M. Stamova, On the Lyapunov theory for functional differential equations of fractional order Proceedings of the American Mathematical Society. ,vol. 144, pp. 1581- 1593 ,(2015) , 10.1090/PROC/12822
Ivanka M. Stamova, Mittag-Leffler stability of impulsive differential equations of fractional order Quarterly of Applied Mathematics. ,vol. 73, pp. 525- 535 ,(2015) , 10.1090/QAM/1394
Luciano Stefanini, Barnabás Bede, Generalized Hukuhara differentiability of interval-valued functions and interval differential equations Nonlinear Analysis: Theory, Methods & Applications. ,vol. 71, pp. 1311- 1328 ,(2009) , 10.1016/J.NA.2008.12.005
D. O'Regan, Multivalued differential equations in Banach spaces Computers & Mathematics with Applications. ,vol. 38, pp. 109- 116 ,(1999) , 10.1016/S0898-1221(99)00218-7
Roshdi Khalil, Mohammed Al Horani, Abdelrahman Yousef, Mohammad Sababheh, None, A new definition of fractional derivative Journal of Computational and Applied Mathematics. ,vol. 264, pp. 65- 70 ,(2014) , 10.1016/J.CAM.2014.01.002
Thabet Abdeljawad, On conformable fractional calculus Journal of Computational and Applied Mathematics. ,vol. 279, pp. 57- 66 ,(2015) , 10.1016/J.CAM.2014.10.016
Klaus Deimling, Multivalued Differential Equations ,(1992)
Soheil Salahshour, Ali Ahmadian, Fudzial Ismail, Dumitru Baleanu, Norazak Senu, A New fractional derivative for differential equation of fractional order under interval uncertainty Advances in Mechanical Engineering. ,vol. 7, pp. 1687814015619138- ,(2015) , 10.1177/1687814015619138