General Fractional Integrals and Derivatives of Arbitrary Order

被引：70
|
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：
SYMMETRY-BASEL | 2021年 / 13卷 / 05期
关键词：
Sonine kernel; general fractional derivative of arbitrary order; general fractional integral of arbitrary order; first fundamental theorem of fractional calculus; second fundamental theorem of fractional calculus; CALCULUS;
D O I：
10.3390/sym13050755
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
In this paper, we introduce the general fractional integrals and derivatives of arbitrary order and study some of their basic properties and particular cases. First, a suitable generalization of the Sonine condition is presented, and some important classes of the kernels that satisfy this condition are introduced. Whereas the kernels of the general fractional derivatives of arbitrary order possess integrable singularities at the point zero, the kernels of the general fractional integrals can-depending on their order-be both singular and continuous at the origin. For the general fractional integrals and derivatives of arbitrary order with the kernels introduced in this paper, two fundamental theorems of fractional calculus are formulated and proved.
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页数：14
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