Una nota sobre el problema de las curvas geodésicas con derivada fraccionaria de Atangana–Baleanu
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https://doi.org/10.29057/icbi.v13iEspecial.13480Palabras clave:
operadores fraccionaria, integración por partes, cálculo de variaciones, curvas geodésicasResumen
Este artículo presenta algunas propiedades y relaciones que existen entre los operadores fraccionarios en el sentido de Riemann–Liouville y de Atangana–Baleanu. En particular, se presenta una demostración de la fórmula de integración por partes cuando la derivada fraccionaria de Atangana–Baleanu es considerada. Como una aplicación de estas propiedades, se analiza el problema clásico de la determinación de las curvas geodésicas en el plano considerando la derivada fraccionaria de Atangana–Baleanu. La introducción de la derivada fraccionaria en el funcional que describe el problema de optimización se realiza mediante el método de fraccionalización. Los resultados obtenidos se comparan con el problema clásico.
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Abdeljawad, T., Atangana, A., Gómez-Aguilar, J. F., and Jarad, F. (2019). On a more general fractional integration by parts formulae and applications. Physica A: Statistical Mechanics and its Applications, 536:122494. https://doi.org/10.1016/j.physa.2019.122494.
Abdeljawad, T. and Baleanu, D. (2017). Integration by parts and its applications of a new nonlocal fractional derivative with Mittag–Leffler nonsingular kernel. Journal of Nonlinear Sciences and Applications, 10(3):1098–1107. http://doi.org/10.22436/jnsa.010.03.20.
Agrawal, O. P. (2002). Formulation of Euler–Lagrange equations for fractional variational problems. Journal of Mathematical Analysis and Applications, 272(1):368–379. https://doi.org/10.1016/S0022-247X(02)00180-4.
Almeida, R., R. A. C. Ferreira, and D. F. M. Torres (2012). Isoperimetric problems of the calculus of variations with fractional derivatives. Acta Mathematica Scientia, 32(2):619–630. https://doi.org/10.1016/S0252-9602(12)60043-5.
Atanackovic, T. M., Pilipovic, S., Stankovic, B., and Zorica, D. (2014). Fractional calculus with applications in mechanics. Wave propagation, impact and variational principles. John Wiley & Sons, Ltd, Great Britain. https://doi.org/10.1002/9781118909065.
Atangana, A. and Balenu, D. (2016). New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model. Thermal Science, 20(2):763–769. https://doi.org/10.2298/TSCI160111018A.
Baleanu, D. (2009). Fractional variational principles in action. Physica Scripta, 2009(T136):014006. https://doi.org/10.1088/0031-8949/2009/T136/014006.
Baleanu, D. and Fernandez, A. (2018). On some new properties of fractional derivatives with Mittag–Leffler kernel. Communications in Nonlinear Science and Numerical Simulation, 59:444–462. https://doi.org/10.1016/j.cnsns.2017.12.003.
Baleanu, D. and Fernandez, A. (2019). On fractional operators and their classifications. Mathematics, 7(9):830. https://doi.org/10.3390/math7090830.
Bartle, R. G. (19995). The elements of integration and Lebesgue measure. Wiley Classics Library. John Wiley & Sons, Inc., New York. https://doi.org/10.1002/9781118164471.
Brezis, H. (2011). Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York. https://doi.org/10.1007/978-0-387-70914-7.
Caputo, M. and Fabrizio, M. (2015). A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2):73–85.
Chatibi, Y., El Kinani, E. H., and Ouhadan, A. (2019). Variational calculus involving nonlocal fractional derivative with Mittag–Leffler kernel. Chaos, Solitons & Fractals, 118:117–121. https://doi.org/10.1016/j.chaos.2018.11.017.
Coronel-Escamilla, A., Gómez-Aguilar, J. F., Baleanu, D., Escobar-Jiménez, R. F., Olivares-Peregrino, V. H., and Abundez-Pliego, A. (2016). Formulation of Euler-Lagrange and Hamilton equations involving fractional operators with regular kernel. Advances in Difference Equations, 2016(1):283. https://doi.org/10.1186/s13662-016-1001-5.
Freguglia, P. and Giaquinta, M. (2016). The early period of the calculus of variations. Birkhäuser Cham, Switzerland. https://doi.org/10.1007/978-3-319-38945-5.
Gómez-Aguilar, J. F., Razo-Hernández, R., and Granados-Lieberman, D. (2014). A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response. Revista Mexicana de Física, 60(1):32–38.
Gorenflo, R., Kilbas, A. A., Mainardi, F., and Rogosin, S. (2020). Mittag–Leffler functions, related topics and applications. Springer Monographs in Mathematics. Springer, Germany, 2 edition. https://doi.org/10.1007/978-3-662-43930-2.
Lebedev, N. N. (1965). Special functions an their applications. Prentice-Hall,Inc., New York.
Miller, K. S. and Ross, B. (1993). An introduction to the fractional calculus and fractional differential equations. John Wiley & Sons, Inc., New York.
Oldham, K. B. and Spanier, J. (1974). The fractional calculus: Theory and applications of differentiation and integration to arbitrary order, volume 111 of Mathematics in Science and Engineering. Academic Press, Inc., New York.
Podlubny, I., Magin, R. L., and Trymorush, I. (2017). Niels Henrik Abel and the birth of fractional calculus. Fractional Calculus and Applied Analysis, 20(5):1068–1075. https://doi.org/10.1515/fca-2017-0057.
Riewe, F. (1996). Nonconservative Lagrangian and Hamiltonian mechanics. Physical Review E, 53(2):1890–1899. https://doi.org/10.1103/PhysRevE.53.1890.
Riewe, F. (1997). Mechanics with fractional derivatives. Physical Review E, 55:3581–3592. https://doi.org/10.1103/PhysRevE.55.3581.
Ross, B. (1975). A brief history and exposition of the fundamental theory of fractional calculus. In Fractional Calculus and Its Applications, volume 457 of Lecture Notes in Mathematics, pages 1–36. Springer, Berlin. https://doi.org/10.1007/BFb0067096.
Sales-Teodoro, G., Tenreiro-Machado, J. A., and Capelas de Oliveira, E. (2019). A review of definitions of fractional derivatives and other operators. Journal of Computational Physics, 388:195–208. https://doi.org/10.1016/j.jcp.2019.03.008.
Samko, S. G., Kilbas, A. A., and Marichev, O. I. (1993). Fractional integrals and derivatives. Gordon and Breach Science Publishers, Switzerland.
Troutman, J. L. (1996). Variational calculus and optimal control. Undergraduate Texts in Mathematics. Springer New York, NY, New ork, 2 edition. https://doi.org/10.1007/978-1-4612-0737-5.
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