Computational Approach for Differential Equations with Local and Nonlocal Fractional-Order Differential Operators

Kamran, Ujala Gul, Fahad M. Alotaibi, Kamal Shah, Thabet Abdeljawad and Yusuf Gurefe

Journal of Mathematics, 2023, vol. 2023, 1-27

Abstract: Laplace transform has been used for solving differential equations of fractional order either PDEs or ODEs. However, using the Laplace transform sometimes leads to solutions in Laplace space that are not readily invertible to the real domain by analytical techniques. Therefore, numerical inversion techniques are then used to convert the obtained solution from Laplace domain into time domain. Various famous methods for numerical inversion of Laplace transform are based on quadrature approximation of Bromwich integral. The key features are the contour deformation and the choice of the quadrature rule. In this work, the Gauss–Hermite quadrature method and the contour integration method based on the trapezoidal and midpoint rule are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability to different types of fractional differential equations, numerical accuracy, computational efficiency, and ease of programming and implementation. The performance and efficiency of the methods are demonstrated with the help of figures and tables. It is observed that the proposed methods converge rapidly with optimal accuracy without any time instability.

Date: 2023
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2023/6542787.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2023/6542787.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:6542787

DOI: 10.1155/2023/6542787

Access Statistics for this article

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