General Nonlocal Probability of Arbitrary Order

被引：9

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：

ENTROPY | 2023年 / 25卷 / 06期

关键词：

general fractional calculus; fractional derivatives; fractional integrals; nonlocal probability; probability theory; FRACTIONAL CALCULUS; DERIVATIVES; DISTRIBUTIONS; DIFFUSION; EQUATION;

D O I：

10.3390/e25060919

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Using the Luchko's general fractional calculus (GFC) and its extension in the form of the multi-kernel general fractional calculus of arbitrary order (GFC of AO), a nonlocal generalization of probability is suggested. The nonlocal and general fractional (CF) extensions of probability density functions (PDFs), cumulative distribution functions (CDFs) and probability are defined and its properties are described. Examples of general nonlocal probability distributions of AO are considered. An application of the multi-kernel GFC allows us to consider a wider class of operator kernels and a wider class of nonlocality in the probability theory.

引用

页数：45

共 94 条

[1] Operational Calculus for the General Fractional Derivatives of Arbitrary Order [J].