Towards a non-conformable fractional calculus of n-variables

• Autorzy: Martínez Francisco , Nápoles Juan E. Valdés

Identyfikatory

DOI

10.7862/rf.2020.6

• Języki publikacji: EN

Abstrakty

EN

In this paper we present an extension of the non-conformable local fractional derivative, to the case of functions of several variables. Results analogous to those known from the classic multivariate calculus are presented. To show the strength of this approach, we show an extension of the Second Lyapunov Method to the non-conformable local fractional case.

Słowa kluczowe

EN

function of several variables; fractional partial differential operators

PL

funkcje wielu zmiennych; operatory różniczkowe; operatory cząstkowe; operatory ułamkowe

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2020
• Tom: Vol. 43
• Strony: 87--98
• Opis fizyczny: Biblior. 9 poz.

Twórcy

autor

Martínez Francisco

• Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Cartagena, SPAIN

autor

Nápoles Juan E. Valdés

• Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Corrientes Capital, 3400, ARGENTINA

Bibliografia

• [1] R. Agarwal, S. Hristova, D. O’Regan, Applications of Lyapunov functions to Caputo fractional differential equations, Mathematics 6 (2018) 229; doi:10.3390/math6110229
• [2] T.M. Apostol, Calculus, Volume II, Second edition, Wiley, USA, 1969.
• [3] N.Y. Gozutok, U. Gozutok, Multi-variable conformable fractional calculus, Filomat 32:1 (2018) 45–53.
• [4] P.M. Guzman, L.M. Lugo Motta Bittencourt, J.E. Nápoles V., A note on stability of certain Lienard fractional equation, International Journal of Mathematics and Computer Science 14 (2) (2019) 301–315.
• [5] P.M. Guzman, G. Langton, L.M. Lugo, J. Medina, J.E. Nápoles Valdés, A new definition of a fractional derivative of local type, J. Math. Anal. 9:2 (2018) 88–98.
• [6] R. Khalil, M. Al Horani; A. Yousef, M. Sababheh,A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014) 65–70.
• [7] J.E. Nápoles V., P.M. Guzman, L.M. Lugo, Some new results on nonconformable fractional calculus, Advances in Dynamical Systems and Applications 13 (2) (2018) 167–175.
• [8] J.E. Nápoles V., P.M. Guzman, L.M. Lugo, On the stability of solutions of nonconformable differential equations, Studia Universitatis Babeş-Bolyai Mathematica (to appear).
• [9] N. Sene, Exponential form for Lyapunov function and stability analysis of the fractional differential equations, J. Math. Computer Sci. 18 (2018) 388–397.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).