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, 12. 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∈(0,12).

TIME-FRACTIONAL EQUATIONS WITH REACTION TERMS: FUNDAMENTAL SOLUTIONS AND ASYMPTOTICS

Benedetta Pellacci;
2021

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, 12. 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∈(0,12).
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/420849
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