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Erroneous Applications of Fractional Calculus: The Catenary as a Prototype

Author

Listed:
  • Gerardo Becerra-Guzmán

    (Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Av. Universidad No. 940, Aguascalientes C.P. 20100, Ags, Mexico)

  • José Villa-Morales

    (Departamento de Matemáticas y Física, Universidad Autónoma de Aguascalientes, Av. Universidad No. 940, Aguascalientes C.P. 20100, Ags, Mexico)

Abstract

In this work, we study the equation of the catenary curve in the context of the Caputo derivative. We solve this equation and compare the solution with real physical models. From the experiments, we find that the best approximation is achieved in the classical case. Therefore, introducing a fractional parameter arbitrarily can be detrimental. However, we observe that, when adding a certain weight to the chain, fractional calculus produces better results than classical calculus for modeling the minimum height.

Suggested Citation

  • Gerardo Becerra-Guzmán & José Villa-Morales, 2024. "Erroneous Applications of Fractional Calculus: The Catenary as a Prototype," Mathematics, MDPI, vol. 12(14), pages 1-9, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2148-:d:1431319
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