PUBLISHED AND SUBMITTED PAPERS
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P. M. Carvalho-Neto, A survey on an important inequality to Fractional Differential Equations, Revista Eletrônica Paulista de Matemática, v. 22, p. 246-252, 2022.
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P. M. Carvalho-Neto, Abstract differential equations and Caputo fractional derivative, Semigroup Forum, v. 104, p. 561-583, 2022.
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P. M. Carvalho-Neto, R. Fehlberg Junior, The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces I, Communications on Pure and Applied Mathematics, v. 21, p. 3667, 2022.
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P. M. Carvalho-Neto, R. Fehlberg Junior, On the fractional version of Leibniz rule, On the fractional version of Leibniz rule. Mathematische Nachrichten, v. 294, 2020.
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P. M. Carvalho-Neto, S. F. Gastão, M. F. Lazo, Noether Theorem for fractional variational problems depending on fractional derivatives of functions, Applicable Analysis, Applicable Analysis, v. 2019, p. 1-17, 2019.
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P. M. Carvalho-Neto, R. Fehlberg Junior, Conditions to the absence of blow up solutions to fractional differential equations, Acta Applicandae Mathematicae, v. 2017, p. 1-15, 2017.
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P. M. Carvalho-Neto, G. Planas, Mild solutions to the time fractional Navier-Stokes equations in Rn, J. Differ. Equations 259 (2015) 2948–2980.
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P. M. Carvalho-Neto, P. A. Liboni-Filho, A Mean value theorem for metric spaces, Math. Nachr. 288 (2015) 509–524.
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B. de Andrade, A. N. Carvalho, P. M. Carvalho-Neto, P. M. Rubio, Global solutions and comparison results for semilinear fractional differential equations, Topol. Method. Nonl. An. 45 (2015) 439-469.
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ONGOING WORK AND OTHER PUBLICATIONS
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Work in progress
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P. M. Carvalho-Neto, R. Fehlberg Junior, The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces III (In Progress).
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P. M. Carvalho-Neto, R. Fehlberg Junior, The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II (Submitted).
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P. M. Carvalho-Neto, R. Ponce, An introductory study of dynamics on abstract differential equations with time fractional derivative (In Progress).
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P. M. Carvalho-Neto, C. L. Frota, P, G. P. Torelli, The time-fractional wave equation with acoustic boundary condition (In Progress).
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P. M. Carvalho-Neto, J. G. Mesquita, G. Planas, Global attractor for the two dimensional evolution Navier-Stokes Equations (In Progress).
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P. M. Carvalho-Neto, G. Planas, Mittag-Leffler operators and its limit behavior (In Progress).
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M. Bohner, M. C. Bortolan, P. M. Carvalho-Neto, J. G. Mesquita, Pullback attractors for evolution equations (In Progress)
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P. M. Carvalho-Neto, P. A. Liboni-Filho, A polylogarithm solution to the Epsilon-Delta problem (In Progress).
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Others
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P. M. Carvalho-Neto, Fractional differential equations: a novel study of local and global solutions in Banach spaces, Ph.D. Thesis, Universidade de São Paulo, São Carlos, 2013.
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P. M. Carvalho-Neto, Equações de Navier-Stokes com condições de fronteira tipo Navier de fricção, Dissertação de Mestrado, Universidade de São Paulo, São Carlos, 2009 (in Portuguese).
CURRENT STUDENTS
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Ph.D Students
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Juan Carlos Oyola Ballesteros (Scholarship - CAPES)
Title: Still untitled (2021 - in progress)
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Pedro Gabriel Papa Torelli (Scholarship - CAPES)
Title: Still untitled (2021 - in progress)
Co-advisor
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Tiago Augusto dos Santos Boza
Title: Still untitled (2020 - in progress)
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Masters Students
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Nicoly Longaretti De Souza
Title: Still untitled (2023 - in progress)
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Ricardo Machado da Motta. (Scholarship - FAPESC)
Title: Still untitled (2022 - in progress)
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Daniel José Kmita
Title: Still untitled (2021 - in progress)
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Luciano Bento da Silva Junior (Scholarship - CAPES)
Title: A Integral Fracionária de Riemann-Liouville sobre os Espaços Lp (2021 - in progress)
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Undergraduate Dissertation
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None at this time.
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Undergraduate Research
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Rodrigo Alois Muhr Stefanes
Title: Um Estudo da Análise Funcional (2023 - in progress)
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FORMER STUDENTS
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Ph.D Students
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Masters Students
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Marduck Montoya Henao (Scholarship - CNPq)
Title: Problemas fracionários de Cauchy com operadores quase setoriais (03/2016 - 03/2018)
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Ever Elias Vásquez Álvarez (Scholarship - Capes)
Title: Um Estudo das Equações de Navier-Stokes com Condições de Fronteira de Tipo Navier (03/2017 - 03/2019)
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José Guilherme Simion Antunes (Scholarship - Capes)
Title: As Equações de Navier-Stokes 2D Sobre Alguns Domínios Ilimitados: Existência, Unicidade e Estudo do Atrator Global (03/2017 - 03/2019)
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Undergraduate Dissertation
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Ricardo Machado da Motta
Title: Espaços de Lorentz e o Teorema da Interpolação de Marcinkiewicz (2021 - 2022)
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Undergraduate Research
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Ricardo Machado da Motta (Scholarship - CNPq)
Title: Um Estudo dos Espaços de Lorentz (2021 - 2022)
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Ricardo Machado da Motta (Scholarship - CNPq)
Title: Algumas Propriedades das Integrais Fracionárias (2020 - 2021)
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Vinicius Douglas Cerutti
Title: Um Estudo da Análise Funcional (2020 - 2021)
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Vinicius Douglas Cerutti
Title: Sistemas Dinâmicos Não-Lineares (2019 - 2020)
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Júlio Veloso Junior
Title: Topologia Geral (2019 - 2020)
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Tiago Vota Cucco (Scholarship - CNPq)
Title: Um Estudo das Equações Diferenciais (2019 - 2020)
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Tiago Vota Cucco (Scholarship - PET)
Title: Um Estudo dos Espaços Métricos (2018 - 2019)
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Felipe Gabriel
Title: Introdução ao cálculo fracionário (2017 - 2018)
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Lucas Eduardo Oliveira Cândido
Title: Teoria da medida e espaços de Sobolev (2017 - 2018)
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João Rafael de Melo Ruiz
Title: Introdução ao cálculo fracionário (2016 - 2017)
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Lucas Eduardo Oliveira Cândido (Scholarship - CNPq)
Title: Um estudo das equações diferenciais (2016 - 2017)
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