THEORETICAL AND COMPUTATIONAL RESULTS FOR MIXED TYPE VOLTERRA-FREDHOLM FRACTIONAL INTEGRAL EQUATIONS

被引：5

作者：

Amin, Rohul ^{[1
]}

Alrabaiah, Hussam ^{[2
,3
]}

Mahariq, Ibrahim ^{[4
]}

Zeb, Anwar ^{[5
]}

机构：

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

[2] Tafila Tech Univ, Dept Math, Tafila, Jordan

[3] Al Ain Univ, Coll Engn, Al Ain, U Arab Emirates

[4] Amer Univ Middle East, Coll Engn & Technol, Kuwait, Kuwait

[5] COMSATS Univ Islamabad, Dept Math, Abbotabad Campus, Khyber Pakhtunkhawa, Pakistan

来源：

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2022年 / 30卷 / 01期

关键词：

FIEs; Volterra-Fredholm Integral Equations; Existence Result; HWCT; CPs; NUMERICAL-SOLUTION; INTEGRODIFFERENTIAL EQUATIONS; COLLOCATION; STABILITY;

D O I：

10.1142/S0218348X22400357

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we develop a numerical method for the solutions of mixed type Volterra-Fredholm fractional integral equations (FIEs). The proposed algorithm is based on Haar wavelet collocation technique (HWCT). Under certain conditions, we prove the existence and uniqueness of the solution. Also, some stability results are given of Hyers-Ulam (H-U) type. With the help of the HWCT, the considered problem is transformed into a system of algebraic equations which is then solved for the required results by using Gauss elimination algorithm. Some numerical examples for convergence of the proposed technique are taken from the literature. Maximum absolute and root mean square errors are calculated for different collocation points (CPs). The results show that the HWCT is an effective method for solving FIEs. The convergence rate for different CPS is also calculated, which is nearly equal to 2.

引用

页数：9

共 39 条

[31] The regularizing properties of the composite trapezoidal method for weakly singular Volterra integral equations of the first kind [J].