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Fractional Calculus: Historical Notes Apuntes Históricos del Cálculo Fraccionario

  • Vivas Cortez, Miguel ; Guzman, Paulo M. [1] ; Lugo, Luciano M [1] ; Nápoles V, Juan E. [1]
    1. [1] Universidad Nacional del Nordeste

      Universidad Nacional del Nordeste

      Argentina

  • Localización: MATUA: Revista de matemática de la universidad del Atlántico, ISSN-e 2389-7422, Vol. 8, Nº. 2, 2021 (Ejemplar dedicado a: Revista MATUA)
  • Idioma: inglés
  • Enlaces
  • Resumen
    • español

      En este trabajo, presentamos algunos apuntes históricos del cálculo fraccionario Local, y destacamos algunas propiedades y aplicaciones de estas nuevas herramientas matemicas

    • English

      In this paper, we present some historical notes to Generalized Calculus, sometimes called Local Fractional Calculus, and highlight some properties and applications of these new mathematical tools

  • Referencias bibliográficas
    • T. Abdeljawad. On conformable fractional calculus, J. of Computational and Applied Mathematics 279, 2015, 57-66.
    • A. Atangana, Derivative with a New Parameter Theory, Methods and Applications. Academic Press, 2016.
    • A. Atangana, Extension of rate of change concept: From local to nonlocal operators with applications., Results in Physics, 19, 2020, Article...
    • D. Baleanu, COMMENTS ON: ”The failure of certain fractional calculus operators in two physical models”by M. Ortigueira, V. Martynyuk, M. Fedula,...
    • D. Baleanu, A. Fernandez, On Fractional Operators and Their Classifications, Mathematics. 7(9)(2019) 830, 1-10
    • Capelas de Oliveira, E., Tenreiro Machado, J.A. A Review of Definitions for Fractional Derivatives and Integral. Mathematical Problems in...
    • W. Chen. Time-space fabric underying anomalous diffusion, Chaos, Solitons and Fractals 28, 2006, 923-929.
    • J. G. Delgado, J. E. Napoles ´ Valdez, , E. P. Reyes , M. Vivas-Cortez. The Minkowski Inequality for Generalized Fractional Integrals. Appl....
    • A. Fleitas, J. E. Napoles, ´ J. M. Rodr´ıguez, J. M. Sigarreta. On the generalized fractional derivative, submited.
    • F. Gao, X. Yang, Z. Kang. Local fractional Newton method derived from modified local fractional calculus, Proc. of CSO 2009, 2009, 228– 232.
    • P. M. Guzman, ´ P. Korus, ´ J. E. Napoles ´ Valdes, ´ Generalized Integral Inequalities of Chebyshev Type, Fractal Fract. 4, (2020), 100 ,...
    • Guzman, ´ P. M., Langton, G., Lugo, L. M., Medina, J. and Napoles ´ Valdes, ´ J. E., A new definition of a fractional derivative of local...
    • P. M. Guzman, ´ L. M. Lugo, J. E. Napoles, ´ On the stability of solutions of fractional non conformable differential equations, Stud. Univ....
    • P. M. Guzman, ´ J. E. Napoles, ´ Y. Gasimov, Integral inequalities within the framework of generalized fractional integrals, Fractional Differential...
    • J. H. He. A new fractal derivation, Thermal Science 15(1), 2011, 145-147.
    • A. Karci, Chain Rule for Fractional Order Derivatives, Science Innovation, 4(6), 2015, 63-67.
    • U. N. Katugampola, A new fractional derivative with classical properties, arXiv:1410.6535v2 [math.CA] 2014, 1-15.
    • V. N. Katugampola. A new fractional derivative with classical properties, J. of the Amer. Math. Soc. 2014, in press, arXiv:1410.6535.
    • Khalil, R., Al Horani, M., Yousef, A., Sababheh, M., A new definition of fractional derivative. J. Comput. Appl. Math., 264, 2014, 65-70.
    • K. M. Kolwankar, A. D. Gangal. Fractional differentiability of nowhere differentiable functions and dimensions, Chaos 6 (4), 1996, 505-513.
    • K. M. Kolwankar, A. D. Gangal. Holder exponents of irregular signals and local fractional derivatives, Pramana, 48(1), 1997, 49-68.
    • K. M. Kolwankar, A. D. Gangal. Local fractional Fokker-Planck equation, Phys. Rev. Lett. 80, 1996, 214-2020.
    • P. Korus, ´ L. M. Lugo, J. E. Napoles ´ Valdes, ´ Integral inequalities in a generalized context, Studia Scientiarum Mathematicarum Hungarica,...
    • L. M. Lugo, J. E. Napoles ´ Valdes, ´ M. Vivas-Cortez, On the oscillatory behaviour of some forced nonlinear generalized differential equation,...
    • L. M. Lugo, J. E. Napoles ´ Valdes, ´ M. Vivas-Cortez, A multi-index generalized derivative. Some introductory notes, submited
    • Machado, J.T., Kiryakova, V., Mainardi, F. Recent history of fractional calculus. Commun. Nonlinear Sci. Numer. Simul. 16, 2011, 1140–1153.
    • Martínez, F., Mohammed, P.O., Napoles ´ Valdes, ´ J.E. Non Conformable Fractional Laplace Transform., Kragujevac J. of Math. 46(3), 2022,...
    • Martínez, F., Napoles ´ Valdes, ´ J. E., Towards a Non-Conformable Fractional Calculus of N-variables, Journal of Mathematics and Applications,...
    • A. B. Mingarelli, On generalized and fractional derivatives and their applications to classical mechanics, arXiv:submit/2328320 [math-ph],...
    • J. E. Napoles ´ Valdes, ´ Y. S. Gasimov, A. R. Aliyeva, On the Oscillatory Behavior of Some Generalized Differential Equation, Punjab University...
    • Napoles ´ Valdes, ´ J. E., Guzman, ´ P. M. and Lugo, L. M., Some New Results on Nonconformable Fractional Calculus, Advances in Dynamical...
    • Napoles, ´ J.E., Guzman, ´ P. M., Lugo, L. M., Kashuri, A., The local generalized derivative and Mittag Leffler function, Sigma J Eng &...
    • J. E. Napoles, ´ M. N. Quevedo, On the Oscillatory Nature of Some Generalized Emden-Fowler Equation, Punjab University Journal of Mathematics,...
    • J. E. Napoles, ´ M. N. Quevedo, A. R. Gomez ´ Plata, ONn the asymptotic behaviour of a generalized nonliear differential equation , Sigma...
    • J. E. Napoles, ´ J. M. Rodr´ıguez, J. M. Sigarreta, On Hermite-Hadamard type inequalities for nonconformable integral operators., Symmetry...
    • J. E. Napoles, ´ C. Tunc, On the boundedness and oscillation of non conformable Lienard Equation, Journal of Fractional Calculus and Applications,...
    • A. Parvate, A. D. Gangal. Calculus on fractal subsets of real line - I: formulation. Fractals 17 (1), 2009, 53-81.
    • E. Reyes-Luis, G. Fernandez-Anaya, ´ J. Chav´ ez-Carlos, L. Diago-Cisneros, R. Munoz-V ˜ ega, A twoindex generalization of conformable operators...
    • A. Tallafha, S. Al Hihi, Total and directional fractional derivatives, Intern.l J. Pure and Applied Math., 107(4), 2016, 1037-1051.
    • S. Umarov, S. Steinberg, Variable order differential equations with piecewise constant order–function and diffusion with changing modes. Z....
    • J. Vanterler da C. Sousa, E. Capelas de Oliveira, A new truncated M-fractional derivative type unifying some fractional derivative types with...
    • J. Vanterler da C. Sousa, E. Capelas de Oliveira, M-fractional derivative with classical properties, Submitted, (2017).
    • M. Vivas-Cortez, P. Korus, ´ J. E. Napoles ´ Valdes, ´ Some generalized Hermite-Hadamard-Fejer´ inequality for convex functions, Advances...
    • M. Vivas-Cortez, J. E. Napoles ´ Valdes, ´ L. M. Lugo, On a Generalized Laplace Transform, Appl. Math. Inf. Sci. 15(5), 2021, 667-675
    • M. Vivas-Cortez, J. E. Hernandez ´ Hernandez, ´ On a Hardy’s inequality for a fractional integral operator. Annals of the University of Craiova,...
    • M. Vivas-Cortez, J. E. Hernandez ´ Hernandez, ´ Hermite-Hadamard Inequalities type for Raina’s fractional integral operator using η−convex...
    • M. Vivas-Cortez, A. Kashuri, R. Liko, J. E. Hernandez ´ Hernandez, ´ Trapezium-Type Inequalities for an Extension of Riemann-Liouville Fractional...
    • M. Vivas-Cortez , A. Kashuri, J. E. Hernandez ´ Hernandez, ´ Trapezium-Type Inequalities for Raina’s Fractional Integrals Operator Using Generalized...
    • M. Vivas-Cortez, M. Aamir Ali, H. Budak, H. Kalsoom, P. Agarwal. Some New Hermite-Hadamard and related inequalities for convex functions via...
    • X. J. Yang, Local Fractional Integral Transforms. Progress in Nonlinear Science, 4, 2011, 1-225.
    • X. J. Yang, Local Fractional Functional Analysis and Its Applications. Asian Academic publisher Limited, Hong kong, China. 2011.
    • X. J. Yang et al., Transport Equations in Fractal Porous Media within Fractional Complex Transform Method, Proceedings, Romanian Academy,...
    • X. J. Yang et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
    • X. J. Yang et al., A New Local Fractional Derivative and Its Application to Diffusion in Fractal Media, Computational Method for Complex Science,...
    • D. Zhao, M. Luo, General conformable fractional derivative and its physical interpretation. Calcolo 54 , 2017, 903–917.
    • Zulfeqarr, F., (2017) Ujlayan, A. and Ahuja, A. A new fractional derivative and its fractional integral with some applications, arXiv: 1705.00962v1...

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