Scale-Invariant General Fractional Calculus: Mellin Convolution Operators

被引：11

作者：

Tarasov, Vasily E. ^{[1
,2
]}

机构：

[1] Lomonosov Moscow State Univ, Skobeltsyn Inst Nucl Phys, Moscow 119991, Russia

[2] Natl Res Univ, Moscow Aviat Inst, Dept Phys, 915, Moscow 125993, Russia

来源：

FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 06期

关键词：

fractional calculus; general fractional calculus; Hadamard fractional derivative; DERIVATIVES; DYNAMICS; INTEGRATION; TRANSFORM; EQUATIONS;

D O I：

10.3390/fractalfract7060481

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

General fractional calculus (GFC) of operators that is defined through the Mellin convolution instead of Laplace convolution is proposed. This calculus of Mellin convolution operators can be considered as an analogue of the Luchko GFC for the Laplace convolution operators. The proposed general fractional differential operators are generalizations of scaling (dilation) differential operator for the case of general form of nonlocality. Semi-group and scale-invariant properties of these operators are proven. The Hadamard and Hadamard-type fractional operators are special case of the proposed operators. The fundamental theorems for the scale-invariant general fractional operators are proven. The proposed GFC can be applied in the study of dynamics, which is characterized by nonlocality and scale invariance.

引用

页数：25

共 91 条

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