@article{Nguyen2022, 
author = {Anh Tuan Nguyen and Chao Yang},
title = {On a time-space fractional diffusion equation with a semilinear source of exponential type},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {4},
pages = {1354-1373},
keywords = {global well-posedness, Caputo derivative, Exponential nonlinearity, time-space fractional diffusion},
url = {https://www.sciopen.com/article/10.3934/era.2022071},
doi = {10.3934/era.2022071},
abstract = {In the current paper, we are concerned with the existence and uniqueness of mild solutions to a Cauchy problem involving a time-space fractional diffusion equation with an exponential semilinear source. By using the iteration method and some  Lp−Lq-type estimates of fundamental solutions associated with the Mittag-Leffler function, we study the well-posedness of the problem in two different cases corresponding to two assumptions on the Cauchy data. On the one hand, when considering initial data in  Lp(RN)∩L∞(RN), the problem possesses a local-in-time solution. On the other hand, we obtain a global existence result for a mild solution with small data in an Orlicz space.}
}