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

We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. also focus on one-dimensional spatial setting case which exponent is equal to, or larger than, \begin{document}$ \frac12 $\end{document}. In this situation, we prove that speed invasion at least "almost square root type", namely it than id="M2">\begin{document}$ ct^\beta $\end{document} for any given id="M3">\begin{document}$ c>0 id="M4">\begin{document}$ \beta\in\left(0,\frac12\right)