On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method
Abstract
1. Introduction
2. Preliminaries
- for all and , where and are constants;
- for all and , where c is constant;
- for all .
- ;
3. The Methodology of the LRPSM
4. Approximate Solutions
5. Numerical Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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AE (LRPSM) | AE (NTDM) [32] | AE (RPSM) [33] | |
---|---|---|---|
0 | 0 | 0 | |
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Damag, F.H.; Saif, A. On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method. Fractal Fract. 2025, 9, 301. https://doi.org/10.3390/fractalfract9050301
Damag FH, Saif A. On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method. Fractal and Fractional. 2025; 9(5):301. https://doi.org/10.3390/fractalfract9050301
Chicago/Turabian StyleDamag, Faten H., and Amin Saif. 2025. "On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method" Fractal and Fractional 9, no. 5: 301. https://doi.org/10.3390/fractalfract9050301
APA StyleDamag, F. H., & Saif, A. (2025). On Solving Modified Time Caputo Fractional Kawahara Equations in the Framework of Hilbert Algebras Using the Laplace Residual Power Series Method. Fractal and Fractional, 9(5), 301. https://doi.org/10.3390/fractalfract9050301