Nieto Roig, Juan JoséPimentel Sunio, Johnatan2017-03-152017-03-152017http://hdl.handle.net/10347/15219Fractional calculus, the branch of mathematics dealing with derivatives and integrals of non-integer order, began as a mere mathematical curiosity during the time of Leibniz but through the years has developed into a very dynamic field of research. Famous mathematicians such as Riemann, Liouville, Grunwald, Euler, Lagrange, Caputo and others laid the foundation of the modern theory thus paving the way for fractional calculus to enter mainstream mathematics. At present, this field of study is still developing rapidly. New concepts and ideas such as the Caputo-Fabrizio formulation for example, have emerged and applications in such varied fields as viscoelasticity, fluid flow, rheology, etc., have arisen. In this thesis we will address new problems and issues within this area.engEsta obra atópase baixo unha licenza internacional Creative Commons BY-NC-ND 4.0. Calquera forma de reprodución, distribución, comunicación pública ou transformación desta obra non incluída na licenza Creative Commons BY-NC-ND 4.0 só pode ser realizada coa autorización expresa dos titulares, salvo excepción prevista pola lei. Pode acceder Vde. ao texto completo da licenza nesta ligazón: https://creativecommons.org/licenses/by-nc-nd/4.0/deed.glhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.glFractional calculusCaputo fractional derivativeDifferential equationFixed point theoremMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120210 Funciones de variables realesMaterias::Investigación::12 Matemáticas::1202 Análisis y análisis funcional::120219 Ecuaciones diferenciales ordinariasdoctoral thesisopen access