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

[21] NEW FAMILIES OF SOLUTIONS FOR THE SPACE-TIME FRACTIONAL BURGERS' EQUATION
Hassaballa, Abaker A.
Adam, Ahmed M. A.
Yousif, Eltayeb A.
Nouh, Mohamed I.
JOURNAL OF SCIENCE AND ARTS, 2021, (04) : 919 - 934
[22] A comprehensive numerical study of space-time fractional bioheat equation using fractional-order Legendre functions
Roohi, R.
Heydari, M. H.
Aslami, M.
Mahmoudi, M. R.
EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (10):
[23] Inverse source problems for a space-time fractional differential equation
Ali, Muhammad
Aziz, Sara
Malik, Salman A.
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 2020, 28 (01) : 47 - 68
[24] Local Fuzzy Fractional Partial Differential Equations in the Realm of Fractal Calculus with Local Fractional Derivatives
Osman, Mawia
Marwan, Muhammad
Shah, Syed Omar
Loudahi, Lamia
Samar, Mahvish
Bittaye, Ebrima
Mohammed Mustafa, Altyeb
FRACTAL AND FRACTIONAL, 2023, 7 (12)
[25] EXACT SOLUTIONS OF THE SPACE-TIME FRACTIONAL EQUAL WIDTH EQUATION
Ma, Hongcai
Meng, Xiangmin
Wu, Hanfang
Deng, Aiping
THERMAL SCIENCE, 2019, 23 (04): : 2307 - 2313
[26] New approaches for the solution of space-time fractional Schrodinger equation
Demir, Ali
Bayrak, Mine Aylin
Ozbilge, Ebru
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[27] Numerical solution of the conformable space-time fractional wave equation
Yaslan, H. Cerdik
CHINESE JOURNAL OF PHYSICS, 2018, 56 (06) : 2916 - 2925
[28] Symmetry analysis of space-time fractional Poisson equation with a delay
Nass, Aminu M.
QUAESTIONES MATHEMATICAE, 2019, 42 (09) : 1221 - 1235
[29] A space-time finite element method for fractional wave problems
Li, Binjie
Luo, Hao
Xie, Xiaoping
NUMERICAL ALGORITHMS, 2020, 85 (03) : 1095 - 1121
[30] Asymptotic properties of some space-time fractional stochastic equations
Foondun, Mohammud
Nane, Erkan
MATHEMATISCHE ZEITSCHRIFT, 2017, 287 (1-2) : 493 - 519

← 1 2 3 4 5 →