Existencia de soluciones de la ecuación fraccionaria del péndulo forzado
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Date
2023
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Universidad Nacional de Trujillo
Abstract
El objetivo principal de la presente tesis es contribuir con la base te´orica del C´alculo Fraccionario,
en particular sobre las propiedades de la derivada d´ebil fraccionaria de Riemann-
Liouville y los espacios fraccionarios del tipo Sobolev obtenido con dichas derivadas d´ebiles.
As´ı mismo aplicar estos resultados en la soluci´on de un problema c´oncavo-convexo fraccionario
con derivadas fraccionarias de Riemann-Liouville mixtas, las que son una generalizacion
de la ecuaci´on fraccionaria del p´endulo forzado.
The main objective of this thesis is to contribute with the theoretical basis of the Fractional Calculus, in particular on the properties of the weak fractional derivative of Riemann-Liouville and the fractional spaces of Sobolev type obtained with these weak derivatives. Furthermore, we apply these results in the solution of a fractional concave-convex problem with mixed Riemann-Liouville fractional derivatives, which are a generalization of the fractional equation of the forced pendulum.
The main objective of this thesis is to contribute with the theoretical basis of the Fractional Calculus, in particular on the properties of the weak fractional derivative of Riemann-Liouville and the fractional spaces of Sobolev type obtained with these weak derivatives. Furthermore, we apply these results in the solution of a fractional concave-convex problem with mixed Riemann-Liouville fractional derivatives, which are a generalization of the fractional equation of the forced pendulum.
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Keywords
Péndulo forzado, Métodos variacionales, Operadores fraccionarios de Riemann-
Liouville, Problemas no locales, Espacio de sobolev fraccionario