Analyzing Both Fractional Porous Media and Heat Transfer Equations via Some Novel Techniques

Wedad Albalawi, Rasool Shah, Nehad Ali Shah, Jae Dong Chung (), Sherif M. E. Ismaeel and Samir A. El-Tantawy
Additional contact information
Wedad Albalawi: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Rasool Shah: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
Sherif M. E. Ismaeel: Department of Physics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Samir A. El-Tantawy: Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt

Mathematics, 2023, vol. 11, issue 6, 1-19

Abstract: It has been increasingly obvious in recent decades that fractional calculus (FC) plays a key role in many disciplines of applied sciences. Fractional partial differential equations (FPDEs) accurately model various natural physical phenomena and many engineering problems. For this reason, the analytical and numerical solutions to these issues are seriously considered, and different approaches and techniques have been presented to address them. In this work, the FC is applied to solve and analyze the time-fractional heat transfer equation as well as the nonlinear fractional porous media equation with cubic nonlinearity. The idea of solving these equations is based on the combination of the Yang transformation (YT), the homotopy perturbation method (HPM), and the Adomian decomposition method (ADM). These combinations give rise to two novel methodologies, known as the homotopy perturbation transform method (HPTM) and the Yang tranform decomposition method (YTDM). The obtained results show the significance of the accuracy of the suggested approaches. Solutions in various fractional orders are found and discussed. It is noted that solutions at various fractional orders lead to an integer-order solution. The application of the current methodologies to other nonlinear fractional issues in other branches of applied science is supported by their straightforward and efficient process. In addition, the proposed solution methods can help many plasma physics researchers in interpreting the theoretical and practical results.

Keywords: Yang transformation; fractional porous media; fractional heat transfer equation; homotopy perturbation method; Adomian decomposition method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1350/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1350/ (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:11:y:2023:i:6:p:1350-:d:1093534

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 ().