OPERATIONAL CALCULUS FOR THE GENERAL FRACTIONAL DERIVATIVE AND ITS APPLICATIONS

被引：77
|
作者：
Luchko, Yuri [1 ]
机构：
[1] Beuth Tech Univ Appl Sci Berlin, Dept Math Phys & Chem, Luxemburger Str 10, D-13353 Berlin, Germany
来源：
FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2021年 / 24卷 / 02期
关键词：
Sonine kernels; general fractional derivative; general fractional integral; fundamental theorem for the fractional derivative; operational calculus; fractional differential equations; convolutions; Mittag-Leffler functions; convolution series; INTEGRAL-EQUATION;
D O I：
10.1515/fca-2021-0016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of power function type at the point zero. Both particular cases and compositions of these operators are discussed. Then we proceed with a construction of an operational calculus of the Mikusinski type for the general fractional derivatives with the Sonine kernels. This operational calculus is applied for analytical treatment of some initial value problems for the fractional differential equations with the general fractional derivatives. The solutions are expressed in form of the convolution series that generalize the power series for the exponential and the Mittag-Leffler functions.
引用
收藏
页码：338 / 375
页数：38
相关论文
共 50 条
12345