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Open AccessFeature PaperArticle

Growth Equation of the General Fractional Calculus

1
Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, 01024 Kyiv, Ukraine
2
Department of Mathematics, University of Bielefeld, D-33615 Bielefeld, Germany
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(7), 615; https://doi.org/10.3390/math7070615
Received: 2 May 2019 / Revised: 8 July 2019 / Accepted: 9 July 2019 / Published: 11 July 2019
(This article belongs to the Special Issue Mathematical Economics: Application of Fractional Calculus)
We consider the Cauchy problem ( D ( k ) u ) ( t ) = λ u ( t ) , u ( 0 ) = 1 , where D ( k ) is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory 71 (2011), 583–600), λ > 0 . The solution is a generalization of the function t E α ( λ t α ) , where 0 < α < 1 , E α is the Mittag–Leffler function. The asymptotics of this solution, as t , are studied. View Full-Text
Keywords: generalized fractional derivatives; growth equation; Mittag–Leffler function generalized fractional derivatives; growth equation; Mittag–Leffler function
MDPI and ACS Style

Kochubei, A.N.; Kondratiev, Y. Growth Equation of the General Fractional Calculus. Mathematics 2019, 7, 615.

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