EXACT SOLUTIONS OF NONLINEAR FRACTIONAL CAHN–ALLEN EQUATION ARIES IN DIFFERENT NONLINEAR PHYSICAL PHENOMENON USING UNIFIED TECHNIQUE

Najla A. Mohammed, Md. Nur Alam, Imran Talib, Dennis Ling Chuan Ching, Taghreed A. Assiri, Mohammad Hassan, Sultan Alshehery, Md. Fayz-Al-Asad, A. F. Aljohani, Sehra and Ilyas Khan
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Najla A. Mohammed: Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah, Saudi Arabia
Md. Nur Alam: ��Department of Mathematics, Pabna University of Science and Technology, Pabna 6600, Bangladesh
Imran Talib: ��Department of Mathematics and Statistics, Faculty of Science and Technology, Virtual University of Pakistan, Lahore, Pakistan
Dennis Ling Chuan Ching: �Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS, Perak 32610, Malaysia
Taghreed A. Assiri: Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah, Saudi Arabia
Mohammad Hassan: �Department of Mathematics, Northeastern Regional Institute of Science and Technology, Itanagar, Arunachal Pradesh 791 109, India
Sultan Alshehery: ��College of Engineering, Mechanical Engineering Department, King Khalid University, Abha, Saudi Arabia
Md. Fayz-Al-Asad: *Department of Mathematics, American International University – Bangladesh, Kuratoli, Khilkhet, Dhaka 1229, Bangladesh
A. F. Aljohani: ��†Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
Sehra: ��‡Shaheed Benazir Bhutto Women University, Peshawar 25000, Khyber Pakhtunkhwa, Pakistan
Ilyas Khan: �§Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India¶¶Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, Jordan∥∥Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-23

Abstract: The nonlinear fractional Cahn–Allen (NFCA) equation provides insight into phase modifications and pattern elaboration in natural structures, clarifying how various states of matter have changed throughout time. By using a unified technique, this study aims to present novel, precise solutions to the NFCA problem. This method has led to the discovery of a broad spectrum of soliton solutions, ranging from dark compactons and dark solitons to periodic kink behaviors, rough wave behaviors, and periodic patterns featuring peaked crests and troughs. It has also unveiled anti-kink periodic behaviors, periodic wave behaviors, bright-dark single solitons, periodic patterns displaying anti-peaked crests and anti-troughs, bright solitons, and compound soliton phenomena. Notably, these accomplishments have been made possible through the utilization of Maple software. These findings are important for fractional nonlinear dynamical models (FNLDMs). In order to clarify many dynamic behaviors that solutions of the NFCA equation display in other scientific fields, such as quantum mechanics, mathematical biology, and plasma physics, contour plots and 3D surface representations of these exact solutions are also featured. Through our investigation using the unified technique, we have unveiled a plethora of novel discoveries. Employing this method has revealed a total of 54 fresh findings. In contrast, Javeed et al. [S. Javeed, S. Saif and D. Baleanu, New exact solutions of fractional Cahn–Allen equation and fractional DSW system, Adv. Differential Equations 2018 (2018) 459] applied the first integral technique, resulting in only eight outcomes. Upon comparing their results with ours, our approach has yielded an additional four out of six innovative results. As far as we are aware, the application of our technique to the NFCA equation has not been previously documented. We anticipate that future research will expand this methodology to include other FNLDMs.

Keywords: The Analytical Technique; The Nonlinear Fractional Cahn–Allen Equation; Exact Solutions for Fractional Nonlinear Dynamical Models (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24400619

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