Fractional differential equations: a novel study of local and global solutions in Banach spaces

Author(s)

Paulo Mendes de Carvalho Neto

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2013-05-16

Examining board members

Alexandre Nolasco de Carvalho; Gabriela Del Valle Planas; José Antonio Langa Rosado; Pedro Marin Rubio; Bruno Luis de Andrade Santos

• Advisor: Alexandre Nolasco de Carvalho

Abstract

Motivated by the huge success of the applications of the abstract fractional equations in many areas of science and engineering, and by the unsolved question in this theory, in this work we study several matters related to abstract fractional Cauchy problems of order \'alpha\' \'it belongs\' (0, 1). We search to answer some questions that were open: for instance, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally, by establishing some general comparison results, we apply them to conclude the global well-posedness of a fractional partial differential equation coming from heat conduction theory (AU)