التفاصيل البيبلوغرافية
| العنوان: |
A New Hybrid Optimal Auxiliary Function Method for Approximate Solutions of Non-Linear Fractional Partial Differential Equations. |
| المؤلفون: |
Ashraf, Rashid, Nawaz, Rashid, Alabdali, Osama, Fewster-Young, Nicholas, Ali, Ali Hasan, Ghanim, Firas, Alb Lupaş, Alina |
| المصدر: |
Fractal & Fractional; Sep2023, Vol. 7 Issue 9, p673, 18p |
| مصطلحات موضوعية: |
FRACTIONAL differential equations, PARTIAL differential equations, NONLINEAR differential equations, CAPUTO fractional derivatives, NONLINEAR equations, FRACTIONAL calculus, HYBRID systems, POISSON'S equation |
| مستخلص: |
This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann–Liouville's fractional integral and the Caputo derivative. This approach eliminates the need for assumptions about parameter magnitudes, offering a significant advantage. We validate our approach using the time-fractional Cahn–Hilliard, fractional Burgers–Poisson, and Benjamin–Bona–Mahony–Burger equations. Comparative testing shows that our method outperforms new iterative, homotopy perturbation, homotopy analysis, and residual power series methods. These examples highlight our method's effectiveness in obtaining precise solutions for non-linear fractional differential equations, showcasing its superiority in accuracy and consistency. We underscore its potential for revealing elusive exact solutions by demonstrating success across various examples. Our methodology advances fractional differential equation research and equips practitioners with a tool for solving non-linear equations. A key feature is its ability to avoid parameter assumptions, enhancing its applicability to a broader range of problems and expanding the scope of problems addressable using fractional calculus techniques. [ABSTRACT FROM AUTHOR] |
|
Copyright of Fractal & Fractional is the property of MDPI and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| قاعدة البيانات: |
Complementary Index |
Full Text Finder