ON FRACTAL SPACE-TIME AND FRACTIONAL CALCULUS

被引：96

作者：

Hu, Yue ^{[1
]}

He, Ji-Huan ^{[2
]}

机构：

[1] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo, Peoples R China

[2] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, Suzhou, Peoples R China

来源：

THERMAL SCIENCE | 2016年 / 20卷 / 03期

关键词：

He's fractional derivative; Adomian's decomposition method; variational iteration method; exp-function method; fractional complex transform; fractional Fornberg-Whitham equation; PARTIAL-DIFFERENTIAL-EQUATIONS; SILKWORM COCOON HIERARCHY; HEAT-TRANSFER; NONLINEAR EQUATIONS; ASYMPTOTIC METHODS; COMPLEX TRANSFORM; WOOL FIBER; DIFFUSION; TERMS; MODEL;

D O I：

10.2298/TSCI1603773H

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.

引用

页码：773 / 777

页数：5

共 50 条

[31] Intermittence and Space-Time Fractional Stochastic Partial Differential Equations
Mijena, Jebessa B.
Nane, Erkan
POTENTIAL ANALYSIS, 2016, 44 (02) : 295 - 312
[32] Space-time duality and high-order fractional diffusion
Kelly, James F.
Meerschaert, Mark M.
PHYSICAL REVIEW E, 2019, 99 (02)
[33] A reliable analytical algorithm for space-time fractional cubic isothermal autocatalytic chemical system
Saad, Khaled M.
PRAMANA-JOURNAL OF PHYSICS, 2018, 91 (04):
[34] Homotopy analysis method for space-time fractional differential equations
Zhang, Xindong
Wei, Leilei
Tang, Bo
He, Yinnian
INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW, 2013, 23 (06) : 1063 - 1075
[35] A study of novel optical solutions of the space-time fractional cubic nonlinear Schrodinger equation
Ozkan, Ayten
Ozkan, Erdogan Mehmet
OPTICAL AND QUANTUM ELECTRONICS, 2024, 56 (02)
[36] Fractional optical solitons of the space-time perturbed fractional Gerdjikov-Ivanov equation
Li, Chaochao
Li, Genhao
Chen, Longwei
OPTIK, 2020, 224
[37] LARGE DEVIATION PRINCIPLE FOR A SPACE-TIME FRACTIONAL STOCHASTIC HEAT EQUATION WITH FRACTIONAL NOISE
Yan, Litan
Yin, Xiuwei
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2018, 21 (02) : 462 - 485
[38] EXACT SOLUTIONS OF SPACE-TIME FRACTIONAL (2+1)-DIMENSIONAL BREAKING SOLITON EQUATION
Tian, Yi
Wan, Jian-Xiong
THERMAL SCIENCE, 2021, 25 (02): : 1229 - 1235
[39] Exact solutions to the space-time fractional Schrodinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation
Eslami, Mostafa
Rezazadeh, Hadi
Rezazadeh, Mohammadreza
Mosavi, Seid Saied
OPTICAL AND QUANTUM ELECTRONICS, 2017, 49 (08)
[40] A semilinear problem associated to the space-time fractional heat equation in RN
Cortazar, Carmen
Quiros, Fernando
Wolanski, Noemi
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2024, 63 (09)

← 1 2 3 4 5 →