Haar wavelet method for solution of variable order linear fractional integro-differential equations

被引：11

作者：

Amin, Rohul ^{[1
]}

Shah, Kamal ^{[2
,3
]}

Ahmad, Hijaz ^{[4
,5
]}

Ganie, Abdul Hamid ^{[6
]}

Abdel-Aty, Abdel-Haleem ^{[7
,8
]}

Botmart, Thongchai ^{[9
]}

机构：

[1] Univ Peshawar, Dept Math, Peshawar 25120, Pakistan

[2] Univ Malakand, Dept Math, Khyber Pakhtunkhwa, Pakistan

[3] Prince Sultan Univ, Dept Math & Gen Sci, Riyadh, Saudi Arabia

[4] Istanbul Ticaret Univ, Informat Technol Applicat & Res Ctr, TR-34445 Istanbul, Turkey

[5] Istanbul Ticaret Univ, Fac Humanities & Social Sci, Dept Math, TR-34445 Istanbul, Turkey

[6] Saudi Elect Univ Abha Male, Coll Sci & Theoret Studies, Basic Sci Dept, Abha 61421, Saudi Arabia

[7] Univ Bisha, Coll Sci, Dept Phys, Bisha 61922, Saudi Arabia

[8] Al Azhar Univ, Fac Sci, Phys Dept, Assiut 71524, Egypt

[9] Khon Kaen Univ, Fac Sci, Dept Math, Khon Kaen 40002, Thailand

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 04期

关键词：

variable-order fractional calculus; fixed-point theory; Gauss elimination method; Haar wavelet; numerical approximation; NUMERICAL-SOLUTION; DIFFERENTIAL-EQUATIONS; INTEGRAL-EQUATIONS;

D O I：

10.3934/math.2022301

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we developed a computational Haar collocation scheme for the solution of fractional linear integro-differential equations of variable order. Fractional derivatives of variable order is described in the Caputo sense. The given problem is transformed into a system of algebraic equations using the proposed Haar technique. The results are obtained by solving this system with the Gauss elimination algorithm. Some examples are given to demonstrate the convergence of Haar collocation technique. For different collocation points, maximum absolute and mean square root errors are computed. The results demonstrate that the Haar approach is efficient for solving these equations.

引用

页码：5431 / 5443

页数：13

共 37 条

[1] Solution of third order linear and nonlinear boundary value problems of integro-differential equations using Haar Wavelet method [J].