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Approximate solutions of one-dimensional systems with fractional derivative

Author

Listed:
  • A. Ferrari

    (Departamento de Matemática, CONICET-Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario, Argentina)

  • M. Gadella

    (#x2020;Departamento de Física, Teórica Atómica y Optica and IMUVA, Universidad de Valladolid, 47011 Valladolid, Spain)

  • L. P. Lara

    (#x2021;Instituto de Física Rosario, CONICET-UNR, Bv. 27 de Febrero, S2000EKF Rosario, Santa Fe, Argentina)

  • E. Santillan Marcus

    (#xA7;Departamento de Matemática, Universidad Nacional de Rosario, Av. Pellegrini 250, 2000 Rosario, Argentina)

Abstract

The fractional calculus is useful to model nonlocal phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution of ordinary fractional differential equations. Due to the nonlocality of the fractional derivative, we may establish an equivalence between fractional oscillators and ordinary oscillators with a dissipative term.

Suggested Citation

  • A. Ferrari & M. Gadella & L. P. Lara & E. Santillan Marcus, 2020. "Approximate solutions of one-dimensional systems with fractional derivative," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-17, July.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:07:n:s0129183120500928
    DOI: 10.1142/S0129183120500928
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