Growth Equation of the General Fractional Calculus

被引：48

作者：

Kochubei, Anatoly N. ^{[1
]}

Kondratiev, Yuri ^{[2
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Math, Tereshchenkivska 3, UA-01024 Kiev, Ukraine

[2] Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany

来源：

MATHEMATICS | 2019年 / 7卷 / 07期

关键词：

generalized fractional derivatives; growth equation; Mittag-Leffler function;

D O I：

10.3390/math7070615

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the Cauchy problem (D(k)u)(t)=lambda 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), lambda>0. The solution is a generalization of the function t & x21a6;E alpha(lambda t alpha), where 0<alpha<1, E alpha is the Mittag-Leffler function. The asymptotics of this solution, as t ->infinity, are studied.

引用

页数：8

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