An Efficient Technique of Fractional-Order Physical Models Involving ρ -Laplace Transform

Nehad Ali Shah, Ioannis Dassios, Essam R. El-Zahar and Jae Dong Chung
Additional contact information
Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
Ioannis Dassios: AMPSAS, University College Dublin, D04 V1W8 Dublin, Ireland
Essam R. El-Zahar: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea

Mathematics, 2022, vol. 10, issue 5, 1-16

Abstract: In this article, the ρ -Laplace transform is paired with a new iterative method to create a new hybrid methodology known as the new iterative transform method (NITM). This method is applied to analyse fractional-order third-order dispersive partial differential equations. The suggested technique procedure is straightforward and appealing, and it may be used to solve non-linear fractional-order partial differential equations effectively. The Caputo operator is used to express the fractional derivatives. Four numerical problems involving fractional-order third-order dispersive partial differential equations are presented with their analytical solutions. The graphs determined that their findings are in excellent agreement with the precise answers to the targeted issues. The solution to the problems at various fractional orders is achieved and found to be correct while comparing the exact solutions at integer-order problems. Although both problems are the non-linear fractional system of partial differential equations, the present technique provides its solution sophisticatedly. Including both integer and fractional order issues, solution graphs are carefully drawn. The fact that the issues’ physical dynamics completely support the solutions at both fractional and integer orders is significant. Moreover, despite using very few terms of the series solution attained by the present technique, higher accuracy is observed. In light of the various and authentic features, it can be customized to solve different fractional-order non-linear systems in nature.

Keywords: third-order dispersive equations; new iterative method; ?-Laplace transform; approximate solution; caputo’s derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/5/816/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/5/816/ (text/html)

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:gam:jmathe:v:10:y:2022:i:5:p:816-:d:764018

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().