Study of Fractional-Order Boundary Value Problems Using Nondiscretization Numerical Method

Zareen A. Khan, Sajjad Ahmad, Salman Zeb, Muhammad Yousaf and Yusuf Gurefe

Journal of Mathematics, 2023, vol. 2023, 1-20

Abstract: This paper is devoted to present a numerical scheme based on operational matrices to compute approximate solutions to fractional-order boundary value problems. For the mentioned operational matrices, we utilize fractional-order Bernoulli polynomials. Since fractional-order problems are usually difficult to treat for their corresponding analytical or exact solutions, therefore, we need sophisticated methods to find their best numerical solutions. The presented numerical scheme has the ability to reduce the proposed problem to the corresponding algebraic equations. The obtained algebraic equations are then solved by using the computational software MATLAB for the corresponding numerical results. The used method has the ability to save much more time and also is reliable to secure the proper amount of memory. Several examples are solved by using the considered method. Also, the solutions are compared with their exact solution graphically. In addition, the absolute errors for different scale values are presented graphically. In addition, we compare our results with the results of the shifted Legendre polynomials spectral method.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2023/5581962.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2023/5581962.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5581962

DOI: 10.1155/2023/5581962

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().