1 citations · 1 across the 6 of their papers we have counts for
6 papers
A New approach for the unsteady Stokes equations with time fractional derivative in Bounded Domains
Juan Carlos Oyola Ballesteros, Paulo M. Carvalho-Neto
In this work, we introduce a novel variational framework for the study of the unsteady Stokes equations in a bounded open Lipschitz domain in R^n, involving a Caputo fractional der…
Energy Estimates for Fractional Evolution Equations
Paulo M. Carvalho-Neto, Cicero L. Frota, Juan C. Oyola Ballesteros +1
This work presents a more broadly applicable version of an energy inequality for weak solutions of evolution equations involving fractional time derivatives. Unlike the classical i…
A General Version of Carathéodory's Existence and Uniqueness Theorem
Paulo M. de Carvalho-Neto, Cícero L. Frota, Pedro G. P. Torelli
In this paper, we establish a general version of Carathéodory's existence and uniqueness theorem for a semilinear system of integro-differential equations arising from differential…
On the Initial Boundary Value Problem to the Time-Fractional Wave Equation with Acoustic Boundary Conditions
Paulo M. de Carvalho-Neto, Cícero L. Frota, Pedro G. P. Torelli
This paper is concerned with the study of the well-posedeness for the initial boundary value problem to the time-fractional wave equation with acoustic boundary conditions. The pro…
Abstract Differential Equations and Caputo Fractional Derivative
Paulo M. Carvalho-Neto
In this work I consider the abstract Cauchy problems with Caputo fractional time derivative of order , and discuss the continuity of the respective solutions regarding t…
A Polylogarithm Solution to the Epsilon--Delta Problem
Paulo M. de Carvalho-Neto, Paulo A. Liboni Filho
Let be a continuous real function defined in a subset of the real line. The standard definition of continuity at a point allow us to correlate any given epsilon with a (pos…