Erroneous Applications of Fractional Calculus: The Catenary as a Prototype

Gerardo Becerra-Guzmán and José Villa-Morales ()
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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

Mathematics, 2024, vol. 12, issue 14, 1-9

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.

Keywords: fractional catenary curve; Caputo differential equations; fractional models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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