Scale-Invariant General Fractional Calculus: Mellin Convolution Operators

Fractal and Fractional

article

Vasily E. Tarasov¹ 

[1]Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

[2]Department of Physics, 915, Moscow Aviation Institute, National Research University

关键词: fractional calculus;    general fractional calculus;    Hadamard fractional derivative26A33;    34A08;   

DOI  :  10.3390/fractalfract7060481

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 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.

【 授权许可】

CC BY