Banquet Brango, Carlos AlbertoVillamizar Roa, Élder JesúsGuerra Ramos, Nafer Enrique2022-09-022023-09-012022-09-022022-09-01https://repositorio.unicordoba.edu.co/handle/ucordoba/6520The description of many natural phenomena is given thanks to the theory of differential equations and calculus. The latter has evolved in recent decades into what is known as fractional calculus, consolidating itself as a powerful tool that has largely made up for the limitations of integer calculus. In this work, we use tools from calculus with fractional derivatives in time and space to study an initial value problem for a nonlinear Klein-Gordon-Schrödinger system (KGS) in Rn × R, with n ≥ 1, considering general polynomial nonlinearities including, in particular, the classical Yukawa model describing the interaction between nucleons and scalar mesons. We analyse time decay estimates for the associated linear system and demonstrate the existence of local and global mild solutions of the fractional KGS system with initial data in the framework of weak L p spaces. Finally we study the asymptotic behavior of the global mild solutions.Declaración de Autoría............................................................................................................................................................................................................................................. VResumen........................................................................................................................................................................................................................................................................... IXAgradecimientos....................................................................................................................................................................................................................................................... XIIIIntroducción...................................................................................................................................................................................................................................................................... 11. Preliminares.................................................................................................................................................................................................................................................................. 51.1. Espacios Lp . .................................................................................................................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2. Espacios Lp débiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................................................ 61.3. Funciones de Mittag-Leffler . . . . . . . . . . . . . . . . . . . . . . . . .................................................................................................................................................................. 132. Cálculo Fraccionario............................................................................................................................................................................................................................................. 152.1. Algunos antecedentes . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................................................ 152.2. Integral fraccionaria de Riemann-Liouville . . . . . . . . . . . . . . . .................................................................................................................................................... 173. Sistema Klein-Gordon-Schrödinger (KGS) de orden fraccionario......................................................................................................................................... 213.1. Formulación integral del sistema KGS . . . . . . . . . . . . . . . . . . ....................................................................................................................................................... 233.2. Estimativas lineales de decaimiento temporal . . . . . . . . . . . . . . ............................................................................................................................................ 253.3. Estimativas de las no linealidades del sistema . . . . . . . . . . . . . . ............................................................................................................................................ 303.4. Solución local y global del sistema . . . . . . . . . . . . . . . . . . . . .......................................................................................................................................................... 373.5. Comportamiento asintótico . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................................................................................................ 434. Conclusiones ............................................................................................................................................................................................................................................................474.1. Conclusiones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .............................................................................................................................................................................. 474.2. Trabajos futuros . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................................................... 47Bibliografía .....................................................................................................................................................................................................................................................................49application/pdfspaCopyright Universidad de Córdoba, 2022Trabajo de grado - Maestríainfo:eu-repo/semantics/embargoedAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)Sistema de Klein-Gordon-SchrödingerDerivada de caputoSolución local y globalEspacios Lp débilesKlein-Gordon-Schrödinger systemCaputo derivativeLocal and global solutionsWeak Lp spaces