Pseudospectral method for fourth-order fractional Sturm-Liouville problems

被引：0

作者：

Bin Jebreen, Haifa ^{[1
]}

Hernandez-Jimenez, Beatriz ^{[2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, POB 2455, Riyadh 11451, Saudi Arabia

[2] Univ Pablo de Olavide, Dept Econ Metodos Cuantitat & Hist Econ, Seville 41013, Spain

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 09期

关键词：

Chebyshev cardinal functions; fractional Sturm-Liouville problems; pseudospectral method; CHEBYSHEV CARDINAL FUNCTIONS; EFFICIENT METHOD; EIGENVALUES; EQUATION; MODEL;

D O I：

10.3934/math.20241274

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fourth-order fractional Sturm-Liouville problems are studied in this work. The numerical simulation uses the pseudospectral method, utilizing Chebyshev cardinal polynomials. The presented algorithm is implemented after converting the desired equation into an associated integral equation and gives us a linear system of algebraic equations. Then, we can find the eigenvalues by calculating the roots of the corresponding characteristic polynomial. What is most striking is that the proposed scheme accurately solves this type of equation. Numerical experiments confirm this claim.

引用

页码：26077 / 26091

页数：15

共 37 条

[1] Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method [J].

Afarideh, Alireza ;

Saei, Farhad Dastmalchi ;

Saray, Behzad Nemati .

JOURNAL OF MATHEMATICAL MODELING, 2023, 11 (02) :343-355

[2] Pseudospectral method for solving fractional Sturm-Liouville problem using Chebyshev cardinal functions [J].

Afarideh, Alireza ;

Saei, Farhad Dastmalchi ;

Lakestani, Mehrdad ;

Saray, Behzad Nemati .

PHYSICA SCRIPTA, 2021, 96 (12)

[3]

Al-Gwaiz M., 2008, Sturm-Liouville theory and its applications, DOI DOI 10.1007/978-1-84628-972-9

[4] An efficient method for solving fractional Sturm-Liouville problems [J].

Al-Mdallal, Qasem M. .

CHAOS SOLITONS & FRACTALS, 2009, 40 (01) :183-189

[5] CORRECTION OF NUMEROVS EIGENVALUE ESTIMATES [J].

ANDREW, AL ;

PAINE, JW .

NUMERISCHE MATHEMATIK, 1985, 47 (02) :289-300

[6] A Time Fractional Model With Non-Singular Kernal the Generalized Couette Flow of Couple Stress Nanofluid [J].

Arif, Muhammad ;

Ali, Farhad ;

Khan, Ilyas ;

Nisar, Kottakkaran Sooppy .

IEEE ACCESS, 2020, 8 :77378-77395

[7] On a multiwavelet spectral element method for integral equation of a generalized Cauchy problem [J].

Asadzadeh, M. ;

Saray, B. N. .

BIT NUMERICAL MATHEMATICS, 2022, 62 (04) :1383-1416

[8] An efficient method for computing eigenelements of Sturm-Liouville fourth-order boundary value problems [J].

Attili, B. S. ;

Lesnic, D. .

APPLIED MATHEMATICS AND COMPUTATION, 2006, 182 (02) :1247-1254

[9] Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions [J].

Baranovskii, Evgenii S. .

POLYMERS, 2024, 16 (02)

[10] Boundary value problem for nonlinear fractional differential equations of variable order via Kuratowski MNC technique [J].

Benkerrouche, Amar ;

Baleanu, Dumitru ;

Souid, Mohammed Said ;

Hakem, Ali ;

Inc, Mustafa .

ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)

← 1 2 3 4 →