Existence and numerical analysis using Haar wavelet for fourth-order multi-term fractional differential equations

被引：4

作者：

Amin, Rohul ^{[1
]}

Shah, Kamal ^{[2
,3
]}

Mlaiki, Nabil ^{[2
]}

Yuzbasi, Suayip ^{[4
]}

Abdeljawad, Thabet ^{[2
,5
]}

Hussain, Arshad ^{[6
]}

机构：

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

[2] Prince Sultan Univ, Dept Math & Sci, POB 11586, Riyadh, Saudi Arabia

[3] Univ Malakand, Dept Math, Chakdara Dir L, Kpk, Pakistan

[4] Akdeniz Univ, Fac Sci, Dept Math, Antalya, Turkey

[5] China Med Univ, Dept Med Res, Taichung 40402, Taiwan

[6] Karakoram Int Univ, Dept Math, Hunza Campus, Gilgit Baltistan, Pakistan

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2022年 / 41卷 / 07期

关键词：

Fractional calculus; Haar wavelet; Fixed-point theory; Gauss elimination method; Numerical approximation; COLLOCATION METHOD; INTEGRODIFFERENTIAL EQUATIONS;

D O I：

10.1007/s40314-022-02041-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a numerical technique is developed for the solution of multi-term fractional differential equations (FDEs) upto fourth order by using Haar collocation method (HCM). In Caputo sense, the fractional derivative is defined. The integral involved in the equations is calculated by the method of Lepik. The HCM converts the given multi-term FDEs into a system of linear equations. The convergence of the proposed method HCM is checked on some problems. Mean square root and maximum absolute errors are calculated for different numbers of collocation points(CPs), which are recorded in tables. The exact and approximate solution comparison is also given in figures. The time taken by CPU for numerical results is also given in the tables.

引用

页数：15

共 34 条

[1]

Ahmad I., 2021, Int. J. Appl. Comput. Math., V7, P1

[2] Biorthogonal wavelets on the spectrum [J].