The solution to the Cauchy problem with general convolutional derivative D_(k) is shown to generalize the Mittag-Leffler function, and its asymptotics as t to infinity are derived.
Doetsch, Introduction to the Theory and Applications of the Laplace T ransformation, Springer, Berlin
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Growth Equation of the General Fractional Calculus
The solution to the Cauchy problem with general convolutional derivative D_(k) is shown to generalize the Mittag-Leffler function, and its asymptotics as t to infinity are derived.