Numerical solution of nonlinear mixed Fredholm-Volterra integro-differential equations of fractional order by Bernoulli wavelets

被引：0

作者：

Keshavarz, Elham ^{[1
]}

Ordokhani, Yadollah ^{[1
]}

Razzaghi, Mohsen ^{[2
]}

机构：

[1] Alzahra Univ, Fac Math Sci, Dept Math, Tehran, Iran

[2] Mississippi State Univ, Dept Math & Stat, Mississippi State, MS 39762 USA

来源：

COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS | 2019年 / 7卷 / 02期

基金：

美国国家科学基金会;

关键词：

Bernoulli wavelets; Fractional calculus; Fredholm-Volterra integro-differential equations; Caputo derivative; Operational matrix; HOMOTOPY-PERTURBATION; OPERATIONAL MATRICES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a numerical method for solving a class of nonlinear mixed Fredholm-Volterra integro-differential equations of fractional order is presented. The method is based upon Bernoulli wavelets approximations. The operational matrix of fractional order integration for Bernoulli wavelets is utilized to reduce the solution of the nonlinear fractional integro-differential equations to system of algebraic equations. Illustrative examples are included to demonstrate the efficiency and accuracy of the method.

引用

页码：163 / 176

页数：14

共 36 条

[1] FAST WAVELET TRANSFORMS AND NUMERICAL ALGORITHMS .1. [J].

BEYLKIN, G ;

COIFMAN, R ;

ROKHLIN, V .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (02) :141-183

[2] Haar wavelet method for solving lumped and distributed-parameter systems [J].

Chen, CF ;

Hsiao, CH .

IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS, 1997, 144 (01) :87-94

[3]

Costabile F.A., 2006, Rend. Mat, V26, P1

[4]

Ganji DD, 2006, INT J NONLIN SCI NUM, V7, P411

[5] Assessment of homotopy-perturbation and perturbation methods in heat radiation equations [J].

Ganji, DD ;

Rajabi, A .

INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER, 2006, 33 (03) :391-400

[6]

Golberg A.M., 1979, Solution Methods for Integral Equations: Theory and Applications

[7] Homotopy analysis method for fractional IVPs [J].

Hashim, I. ;

Abdulaziz, O. ;

Momani, S. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (03) :674-684

[8] Adomian decomposition method for solving BVPs for fourth-order integro-differential equations [J].

Hashim, Ishak .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 193 (02) :658-664

[9] Approximate analytical solution for seepage flow with fractional derivatives in porous media [J].

He, JH .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 167 (1-2) :57-68

[10] Homotopy perturbation technique [J].

He, JH .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1999, 178 (3-4) :257-262

← 1 2 3 4 →