We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on the one-dimensional spatial setting in the case in which the time-fractional exponent is equal to, or larger than, 21 . In this situation, we prove that the speed of invasion of the fundamental solution is at least “almost of square root type”, namely it is larger than ctβ for any given c > 0 and β ∈ (0, 21 ).
|Number of pages||19|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - Jan 2021|