NUMERICAL SOLUTION OF THE MULTI-TERM VARIABLE-ORDER SPACE FRACTIONAL NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

被引：1

作者：

Yaslan, H. Cerdik ^{[1
]}

机构：

[1] Pamukkale Univ, Dept Math, Denizli, Turkey

来源：

MISKOLC MATHEMATICAL NOTES | 2021年 / 22卷 / 02期

关键词：

nonlinear multi-term fractional partial differential equation; the variable-order Cap-uto fractional derivative; finite difference method; Newton's method; generalized Laguerre polynomials; CABLE EQUATION;

D O I：

10.18514/MMN.2021.3472

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A numerical approach for solving the multi-term variable-order space fractional nonlinear partial differential equations is proposed. The fractional derivatives are described in the Caputo sense. The numerical approach is based on generalized Laguerre polynomials and finite difference method. The proposed scheme transforms the main problem to a system of nonlinear algebraic equations. The nonlinear system is solved by using Newton's method. The validity and the applicability of the proposed technique are shown by numerical examples.

引用

页码：1027 / 1038

页数：12

共 50 条

[1] A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations
El-Sayed, A. A.
Baleanu, D.
Agarwal, P.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2020, 14 (01): : 963 - 974
[2] Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution
GNS Gesellschaft für numerische Simulation mbH, Am Gauberg 2, 38114 Braunschweig, Germany
不详
J. Eur. Syst. Autom., 2008, 6-8 (665-676):
[3] Numerical solution of multi-term fractional differential equations
Katsikadelis, John T.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2009, 89 (07): : 593 - 608
[4] MAXIMUM PRINCIPLES FOR MULTI-TERM SPACE-TIME VARIABLE-ORDER FRACTIONAL DIFFUSION EQUATIONS AND THEIR APPLICATIONS
Liu, Zhenhai
Zeng, Shengda
Bai, Yunru
FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (01) : 188 - 211
[5] Maximum Principles for Multi-Term Space-Time Variable-Order Fractional Diffusion Equations and their Applications
Liu Zhenhai
Zeng Shengda
Bai Yunru
Fractional Calculus and Applied Analysis, 2016, 19 : 188 - 211
[6] A numerical-analytical solution of multi-term fractional-order differential equations
Kukla, Stanislaw
Siedlecka, Urszula
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (07) : 4883 - 4894
[7] Analysis and numerical solution of a nonlinear variable-order fractional differential equation
Hong Wang
Xiangcheng Zheng
Advances in Computational Mathematics, 2019, 45 : 2647 - 2675
[8] Analysis and numerical solution of a nonlinear variable-order fractional differential equation
Wang, Hong
Zheng, Xiangcheng
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2019, 45 (5-6) : 2647 - 2675
[9] Numerical methods and analysis for a multi-term time-space variable-order fractional advection-diffusion equations and applications
Chen, Ruige
Liu, Fawang
Vo Anh
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 352 : 437 - 452
[10] Numerical solution method for multi-term variable order fractional differential equations by shifted Chebyshev polynomials of the third kind
Tural-Polat, Sadiye Nergis
Dincel, Arzu Turan
ALEXANDRIA ENGINEERING JOURNAL, 2022, 61 (07) : 5145 - 5153

← 1 2 3 4 5 →