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

• Ano de defesa: 2013
• Autor(a) principal: Carvalho Neto, Paulo Mendes de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Análise funcional; Equações diferenciais fracionárias; Equações diferenciais parciais; Fractional differential equations; Funções de Mittag-Leffler; Functional analysis; Mittag-Leffler functions; Partial differential equations
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/55/55135/tde-06062013-145531/

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