Growth Equation of the General Fractional Calculus

Anatoly N. Kochubei and Yuri Kondratiev
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Anatoly N. Kochubei: Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkivska 3, 01024 Kyiv, Ukraine
Yuri Kondratiev: Department of Mathematics, University of Bielefeld, D-33615 Bielefeld, Germany

Mathematics, 2019, vol. 7, issue 7, 1-8

Abstract: We consider the Cauchy problem ( D ( k ) u ) ( t ) = ? 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), ? > 0 . The solution is a generalization of the function t ? E ? ( ? t ? ) , where 0 < ? < 1 , E ? is the Mittag–Leffler function. The asymptotics of this solution, as t ? ? , are studied.

Keywords: generalized fractional derivatives; growth equation; Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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