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SECCIÓN A: CIENCIAS EXACTAS Y FÍSICAS

Vol. 12 Núm. 2 (2020): Volumen 12 Número 2

Cálculo fraccionario para ecuaciones diferenciales

DOI
https://doi.org/10.18272/aci.v12i2.1946
Enviado
agosto 20, 2020
Publicado
2021-05-11

Resumen

En el presente trabajo se estudian dos metodologías distintas para la resolución de ecuaciones diferenciales parciales fraccionarias. La primera metodología consiste en usar la transformada de Laplace mediante la proposición de una solución de tipo producto de funciones.  Por otro lado, la segunda metodología  nos permite integrar directamente sobre la ecuación diferencial parcial fraccionaria. Para finalizar el trabajo, se realiza una discución sobre las limitaciones y libertades de ambos métodos

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Citas

  1. Ansorge, R. & Sonar, T. (2009). Mathematical models of fluid dynamics. Wiley Online Library.
  2. Arfken, G. & Weber, H. (1999). Mathematical methods for physicists. American Association of Physics Teachers.
  3. Spiegelhalter, D., Best, N. & Carlin, B. (2002). Bayesian measures of model com- plexity and fit. Journal of the Royal Statistical Society: Series B (Statistical Metho- dology), 64(4), 583-639.
  4. Edelman, M. (2013). Fractional dynamical systems. doi:10 . 1109 / ICFDA . 2014 . 6967376. eprint: arXiv:1401.0048
  5. Sumelka, W., Zaera, R. & Fern Ìandez-S Ìaez, J. (2015). A theoretical analysis of the free axial vibration of non-local rods with fractional continuum mechanics. Mecca- nica, 50(9), 2309-2323.
  6. Carpinteri, A., Cornetti, P. & Sapora, A. (2014). Nonlocal elasticity: an approach based on fractional calculus. Meccanica, 49 (11), 2551-2569.
  7. Craiem, D., Rojo, F., Atienza, J., Guinea, G. & Armentano, R. (2008). Fractional calculus applied to model arterial viscoelasticity. Latin American applied research, 38(2), 141-145.
  8. Applebaum, D. (2004). L Ìevy processes from probability to finance and quantum groups. Notices of the AMS, 51 (11), 1336-1347.
  9. Tarasova, V. & Tarasov, V. (2016). Elasticity for economic processes with memory: fractional differential calculus approach. Fractional Differential Calculus, 6 (2), 219-232.
  10. El-Ajou, A., Odibat, Z., Momani, S. & Alawneh, A. (2010). Construction of analy- tical solutions to fractional differential equations using homotopy analysis method.
  11. International Journal of Applied Mathematics, 40(2).
  12. Caldero Ìn, M., Rosales, J., Guzm Ìan, R., Gonz Ìalez, A. & Alvarez, J. (2015). El c Ìalculo
  13. diferencial e integral fraccionario y sus aplicaciones. Acta universitaria, 25 (2), 20-27.
  14. Almusharrf, A. (2011). Development of fractional trigonometry and an application
  15. of fractional calculus to pharmacokinetic model.
  16. Abel, N. (1881). Solution de quelques probl`emes `a l"™aide d"™int Ìegrales d Ìefinies. Oeu-
  17. vres, 1, 11-27.
  18. Liouville, J. (1834). M Ìemoire sur le th Ìeor`eme des fonctions compl Ìementaires. Journal
  19. fu ̈r die reine und angewandte Mathematik, 1834 (11), 1-19.
  20. Mun ̃oz, J. M. S. (2011). G Ìenesis y desarrollo del c Ìalculo fraccional. Pensamiento
  21. Matem Ìatico, (1), 4.
  22. Rudin, W. (1964). Principles of mathematical analysis. McGraw-hill New York.
  23. Haubold, H., Mathai, A. & Saxena, R. (2011). Mittag-leffler functions and their
  24. applications. Journal of Applied Mathematics, 2011.
  25. Samko, S., Kilbas, A. & Marichev, O. (1993). Fractional integrals and derivatives.
  26. Gordon y Breach Science Publishers, Yverdon Yverdon-les-Bains, Switzerland.
  27. Almeida, R. (2017). A caputo fractional derivative of a function with respect to another function. Communications in Nonlinear Science and Numerical Simulation,
  28. , 460-481.
  29. Alsaedi, A., Nieto, J. J. & Venktesh, V. (2015). Fractional electrical circuits. Ad- vances in Mechanical Engineering, 7 (12), 1687814015618127.
  30. Baleanu, D., Golmankhaneh, A. K. & Golmankhaneh, A. K. (2009). The dual action of fractional multi time hamilton equations. International Journal of Theoretical Physics, 48 (9), 2558-2569.
  31. Baleanu, D., Golmankhaneh, A. K., Golmankhaneh, A. K. & Nigmatullin, R. R. (2010). Newtonian law with memory. Nonlinear Dynamics, 60 (1-2), 81-86.
  32. Baleanu, D., Gu ̈venc ̧, Z. B. & Machado, J. T. (Eds.). (2010). New trends in nano- technology and fractional calculus applications. Springer. doi:https://doi.org/10. 1007/978-90-481-3293-5
  33. Caputo, M. (2014). The role of memory in modeling social and economic cycles of extreme events. En F. Francesco, M. Ram & M. N. Pietro (Eds.), A handbook of alternative theories of public economics. Edward Elgar Publishing. doi:https: //doi.org/10.4337/9781781004715
  34. Caputo, M. & Cametti, C. (2008). Diffusion with memory in two cases of biological interest. Journal of theoretical biology, 254 (3), 697-703.
  35. Caputo, M., Cametti, C. & Ruggero, V. (2008). Time and spatial concentration profile inside a membrane by means of a memory formalism. Physica A: Statistical Mechanics and its Applications, 387 (8-9), 2010-2018.
  36. Caputo, M. & Fabrizio, M. (2015). Damage and fatigue described by a fractional derivative model. Journal of Computational Physics, 293, 400-408.
  37. Cesarone, F., Caputo, M. & Cametti, C. (2004). Memory formalism in the passive diffusion across a biological membrane. J. Membrane Sci, 250, 79-84.
  38. Podlubny, I. (1998). Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier.
  39. Schiff, J. (2013). The laplace transform: theory and applications. Springer Science & Business Media.
  40. Ferreira, M. & Vieira, N. (2016). Eigenfunctions and fundamental solutions of the fractional laplace and dirac operators: the riemann-liouville case. Complex Analysis and Operator Theory, 10(5), 1081-1100.
  41. Caballero, M. (2019). Una introduccio Ìn a las ecuaciones integrales lineales. Recupe- rado desde https://hdl.handle.net/11441/90001
  42. Molano Cabrera, S. A. & Lesmes Acosta, M. d. C. (2007). La alternativa de fredholm.
  43. Ball Ìen Lo Ìpez, J. & Le Ìon, P. (2017). M Ìetodo de descomposici Ìon de adomian (Tesis
  44. de maestr 퀱a, Universidad EAFIT).