Global solutions to a time-fractional Cauchy problem

By Nguyen Dinh Huy, Nguyen Anh Tuan
DOI: 10.37550/tdmu.EJS/2023.05.419

In the current work, we study a Cauchy problem for a time-fractional pseudo-parabolic
equation with a globally Lipschitz source term. We prove the unique existence of a mild
solution to the problem, by the common Banach fixed point theorem. This solution is
then verified that exists globally in time by Gr¨onwall’s inequality. Compare to previous
works about the similar issuse, we approach in a way that does not require using
weighted spaces. Although our approach share a similar spirit to previous studies, our
method seems to be more precise and natural.