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Iterative Investigation of the Nonlinear Fractional Cahn–Allen and Fractional Clannish Random Walker’s Parabolic Equations by Using the Hybrid Decomposition Method
by
Sarfaraz Ahmed
Sarfaraz Ahmed
Ibtisam Aldawish
Ibtisam Aldawish 
,
Syed T. R. Rizvi
Syed T. R. Rizvi
Aly R. Seadawy
Aly R. Seadawy
1
State Key Laboratory of Intelligent Geotechnics and Tunnelling, Shenzhen University, Shenzhen 518060, China
2
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia
3
Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
4
Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah 41411, Saudi Arabia
5
Basic Sciences Research Center (BSRC), Deanship of Scientific Research, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia
*
Author to whom correspondence should be addressed.
Fractal Fract. 2025, 9(10), 656; https://doi.org/10.3390/fractalfract9100656 (registering DOI)
Submission received: 2 September 2025
/
Revised: 5 October 2025
/
Accepted: 8 October 2025
/
Published: 11 October 2025
Abstract
In this work, we numerically investigate the fractional clannish random walker’s parabolic equations (FCRWPEs) and the nonlinear fractional Cahn–Allen (NFCA) equation using the Hybrid Decomposition Method (HDM). The analysis uses the Atangana–Baleanu fractional derivative (ABFD) in the Caputo sense, which has a nonsingular and nonlocal Mittag–Leffler kernel (MLk) and provides a more accurate depiction of memory and heredity effects, to examine the dynamic behavior of the models. Using nonlinear analysis, the uniqueness of the suggested models is investigated, and distinct wave profiles are created for various fractional orders. The accuracy and effectiveness of the suggested approach are validated by a number of example cases, which also support the approximate solutions of the nonlinear FCRWPEs. This work provides significant insights into the modeling of anomalous diffusion and complex dynamic processes in fields such as phase transitions, biological transport, and population dynamics. The inclusion of the ABFD enhances the model’s ability to capture nonlocal effects and long-range temporal correlations, making it a powerful tool for simulating real-world systems where classical derivatives may be inadequate.
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MDPI and ACS Style
Ahmed, S.; Aldawish, I.; Rizvi, S.T.R.; Seadawy, A.R.
Iterative Investigation of the Nonlinear Fractional Cahn–Allen and Fractional Clannish Random Walker’s Parabolic Equations by Using the Hybrid Decomposition Method. Fractal Fract. 2025, 9, 656.
https://doi.org/10.3390/fractalfract9100656
AMA Style
Ahmed S, Aldawish I, Rizvi STR, Seadawy AR.
Iterative Investigation of the Nonlinear Fractional Cahn–Allen and Fractional Clannish Random Walker’s Parabolic Equations by Using the Hybrid Decomposition Method. Fractal and Fractional. 2025; 9(10):656.
https://doi.org/10.3390/fractalfract9100656
Chicago/Turabian Style
Ahmed, Sarfaraz, Ibtisam Aldawish, Syed T. R. Rizvi, and Aly R. Seadawy.
2025. "Iterative Investigation of the Nonlinear Fractional Cahn–Allen and Fractional Clannish Random Walker’s Parabolic Equations by Using the Hybrid Decomposition Method" Fractal and Fractional 9, no. 10: 656.
https://doi.org/10.3390/fractalfract9100656
APA Style
Ahmed, S., Aldawish, I., Rizvi, S. T. R., & Seadawy, A. R.
(2025). Iterative Investigation of the Nonlinear Fractional Cahn–Allen and Fractional Clannish Random Walker’s Parabolic Equations by Using the Hybrid Decomposition Method. Fractal and Fractional, 9(10), 656.
https://doi.org/10.3390/fractalfract9100656
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