On definition of solution of initial value problem for fractional differential equation of variable order

被引：3

作者：

Zhang, Shuqin ^{[1
]}

Wang, Jie ^{[1
]}

Hu, Lei ^{[2
]}

机构：

[1] China Univ Min & Technol Beijing, Dept Math, Beijing 100083, Peoples R China

[2] Shandong Jiaotong Univ, Sch Sci, Jinan 250357, Peoples R China

来源：

AIMS MATHEMATICS | 2021年 / 6卷 / 07期

基金：

中国国家自然科学基金;

关键词：

variable order Caputo fractional derivative; variable order fractional integral; fractional differential equations; initial value problem; approximate solution; BOUNDARY-VALUE-PROBLEMS; NUMERICAL TECHNIQUE; EXISTENCE; DERIVATIVES;

D O I：

10.3934/math.2021401

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a new definition of continuous approximate solution to initial value problem for differential equations involving variable order Caputo fractional derivative based on the classical definition of solution of integer order (or constant fractional order) differential equation. Some examples are presented to illustrate these theoretical results.

引用

页码：6845 / 6867

页数：23

共 35 条

[1] Boundary value problems for the diffusion equation of the variable order in differential and difference settings [J].

Alikhanov, Anatoly A. .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (08) :3938-3946

[2]

Almeida R., 2019, VARIABLE ORDER FRACT, Vfirst

[3]

[Anonymous], 1995, Anal. Math., DOI DOI 10.1007/BF01911126

[4]

[Anonymous], 1974, The fractional calculus theory and applications of differentiation and integration to arbitrary order, DOI DOI 10.1016/S0076-5392(09)60219-8

[5]

[Anonymous], 1993, Integral Transform Spec. Funct., DOI DOI 10.1080/10652469308819027

[6]

Atangana A., 2017, Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology

[7] Numerical solution of variable order fractional nonlinear quadratic integro-differential equations based on the sixth-kind Chebyshev collocation method [J].

Babaei, A. ;

Jafari, H. ;

Banihashemi, S. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2020, 377

[8]

Bai ZB, 2016, ELECTRON J DIFFER EQ

[9] NUMERICAL SCHEMES WITH HIGH SPATIAL ACCURACY FOR A VARIABLE-ORDER ANOMALOUS SUBDIFFUSION EQUATION [J].

Chen, Chang-Ming ;

Liu, F. ;

Anh, V. ;

Turner, I. .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2010, 32 (04) :1740-1760

[10] Existence of solutions of initial value problems for nonlinear fractional differential equations [J].

Deng, Jiqin ;

Deng, Ziming .

APPLIED MATHEMATICS LETTERS, 2014, 32 :6-12

← 1 2 3 4 →