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We consider the Cauchy problem $(\mathbb D_{(k)} u)(t)=\lambda u(t)$,$u(0)=1$, where $\mathbb D_{(k)}$ is the general convolutional derivativeintroduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory {\bf71} (2011), 583--600), $\lambda >0$. The solution is a generalization of thefunction $t\mapsto E_\alpha (\lambda t^\alpha)$ where $0<\alpha <1$, $E_\alpha$is the Mittag-Leffler function. The asymptotics of this solution, as $t\to\infty$, is studied.

Growth Equation of the General Fractional Calculus