Time-fractional equations with reaction terms: fundamental solutions and asymptotics

Serena Dipierro, Benedetta Pellacci, Enrico Valdinoci, Gianmaria Verzini

Research output: Contribution to journalArticlepeer-review

3 Citations (Web of Science)

Abstract

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 ).

Original languageEnglish
Pages (from-to)257-275
Number of pages19
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume41
Issue number1
DOIs
Publication statusPublished - Jan 2021

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