arXiv subjects
Publications and source records attributed to Paulo M. Carvalho Neto.
In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order $α> 0$ in Bochner-Lebesgue spaces. We specifically address the remaining cases concerning its boundedness when $α> 1/p$. Furthermore, we extend some of our previous results by investigating some non-standard function spaces. Finally, we provide a comprehensive summary of the obtained results.
When addressing ordinary differential equations in infinite dimensional Banach spaces, an interesting question that arises concerns the existence (or non existence) of blowing up solutions in finite time. In this manuscript we discuss this question for the fractional differential equation $cD_t^αu = f(t,u)$ proving that when $f$ is locally Lipschitz, however does not maps bounded sets into bounded sets, we can construct a maximal local solution that not "blows up" in finite time.