TRANSFORMATION OF THE MITTAG-LEFFLER FUNCTION TO AN EXPONENTIAL FUNCTION AND SOME OF ITS APPLICATIONS TO PROBLEMS WITH A FRACTIONAL DERIVATIVE

被引：0
|
作者：
Aliev, F. A. [1 ,2 ]
Aliev, N. A. [1 ]
Safarova, N. A. [1 ]
机构：
[1] Baku State Univ, Inst Appl Math, Z Khalilov Str 23, AZ-1148 Baku, Azerbaijan
[2] ANAS, Inst Informat Technol, Baku, Azerbaijan
来源：
APPLIED AND COMPUTATIONAL MATHEMATICS | 2019年 / 18卷 / 03期
关键词：
Exponential Function; Mittag-Leffler Function; Cauchy Problem; Fractional Derivative; Linear Operator Differential Equations; Invariant Function; Transformation Like Laplace;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For the first time the relation between the Mittag-Leffler function and the ordinary exponential function is given. The results are applied to the construction of a solution of the Cauchy problem for ordinary linear operator differential equations with constant coefficients and fractional derivatives. Also this solution is obtained by means of a transformation like Laplace. The example shows that when the order of the derivatives (fractional) approaches integers then the results coincide with the classical ones.
引用
收藏
页码：316 / 325
页数：10
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