Fractional solution of the catenary curve
Corresponding Author
Leonardo Martínez–Jiménez
Departamento de Estudios Multidisciplinarios, División de ingenierías, Campus Irapuato–Salamanca, Universidad de Guanajuato, Guanajuato, México
Correspondence
Leonardo Martínez-Jiménez, Departamento de Estudios Multidisciplinarios, Divisíon de ingenierías Campus Irapuato-Salamanca, Universidad de Guanajuato, Guanajuato, Mexico.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorJorge Mario Cruz–Duarte
División de ingenierías, Campus Irapuato–Salamanca, Universidad de Guanajuato, Guanajuato, México
Search for more papers by this authorJ. Juan Rosales–García
División de ingenierías, Campus Irapuato–Salamanca, Universidad de Guanajuato, Guanajuato, México
Search for more papers by this authorCorresponding Author
Leonardo Martínez–Jiménez
Departamento de Estudios Multidisciplinarios, División de ingenierías, Campus Irapuato–Salamanca, Universidad de Guanajuato, Guanajuato, México
Correspondence
Leonardo Martínez-Jiménez, Departamento de Estudios Multidisciplinarios, Divisíon de ingenierías Campus Irapuato-Salamanca, Universidad de Guanajuato, Guanajuato, Mexico.
Email: [email protected]
Communicated by: D. Zeidan
Search for more papers by this authorJorge Mario Cruz–Duarte
División de ingenierías, Campus Irapuato–Salamanca, Universidad de Guanajuato, Guanajuato, México
Search for more papers by this authorJ. Juan Rosales–García
División de ingenierías, Campus Irapuato–Salamanca, Universidad de Guanajuato, Guanajuato, México
Search for more papers by this authorAbstract
The catenary curve has been used in a vast number of practical applications, and several mathematical models have been studied to approximate its behavior. This work, motivated by the success of fractional calculus, proposes a fractional model for the catenary curve, using the Caputo-Fabrizio (CF) definition. It was analyzed how the fractional derivative order and the fractional initial condition directly affect the hanging cable shape. It was noticed that the proposed model provides the possibility of describing new scenarios and revealing new information about the system. Therefore, this work gives rise to a new family of curves that can be used in any practical problem involving catenaries, varying at most two parameters.
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