Analytical Investigation of Fractional-Order Cahn–Hilliard and Gardner Equations Using Two Novel Techniques

Mohammed Kbiri Alaoui, Kamsing Nonlaopon, Ahmed M. Zidan, Adnan Khan and Rasool Shah
Additional contact information
Mohammed Kbiri Alaoui: Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Kamsing Nonlaopon: Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Ahmed M. Zidan: Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
Adnan Khan: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Rasool Shah: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan

Mathematics, 2022, vol. 10, issue 10, 1-19

Abstract: In this paper, we used the natural decomposition approach with non-singular kernel derivatives to find the solution to nonlinear fractional Gardner and Cahn–Hilliard equations arising in fluid flow. The fractional derivative is considered an Atangana–Baleanu derivative in Caputo manner (ABC) and Caputo–Fabrizio (CF) throughout this paper. We implement natural transform with the aid of the suggested derivatives to obtain the solution of nonlinear fractional Gardner and Cahn–Hilliard equations followed by inverse natural transform. To show the accuracy and validity of the proposed methods, we focused on two nonlinear problems and compared it with the exact and other method results. Additionally, the behavior of the results is demonstrated through tables and figures that are in strong agreement with the exact solutions.

Keywords: Caputo–Fabrizio and Atangana–Baleanu operators; fractional Cahn–Hilliard equation; fractional Gardner equation; Adomian decomposition method; natural transform (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: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/10/1643/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/10/1643/ (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:10:p:1643-:d:813386

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 ().