Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series
Abstract
:1. Introduction
2. Preliminaries
- 1.
- 2.
- 3.
3. LRPS Methodology
4. Numerical Problem
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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t | x | AE at α = 0.5 | AE at α = 0.75 | AE at α = 1 |
---|---|---|---|---|
0.2 | 0.2215650201 | 0.093544132 | 2.00 | |
0.4 | 0.270620127 | 0.114255061 | 2.00 | |
0.1 | 0.6 | 0.330536170 | 0.139551447 | 3.00 |
0.8 | 0.403717788 | 0.170448522 | 3.00 | |
1 | 0.493102021 | 0.208186295 | 4.00 | |
0.2 | 0.2017453516 | 0.1032370436 | 4.00 | |
0.4 | 0.2464123288 | 0.126094010 | 4.88 | |
0.25 | 0.6 | 0.300968699 | 0.154011572 | 5.97 |
0.8 | 0.367603998 | 0.188110158 | 7.29 | |
1 | 0.448992538 | 0.229758266 | 8.91 |
t | x | AE at α = 0.5 | AE at α = 0.75 | AE at α = 1 |
---|---|---|---|---|
0.2 | 0.3122588000 | 0.0937357454 | 8.0 | |
0.4 | 0.2556558826 | 0.0767443373 | 8.0 | |
0.1 | 0.6 | 0.2093133334 | 0.0628329492 | 6.0 |
0.8 | 0.1713712630 | 0.0514432677 | 5.0 | |
1 | 0.1403069234 | 0.0421181854 | 3.0 | |
0.2 | 0.544332261 | 0.176001462 | 2.88 | |
0.4 | 0.4456615616 | 0.1440978086 | 2.358 | |
0.25 | 0.6 | 0.3648768263 | 0.1179773077 | 1.930 |
0.8 | 0.2987358784 | 0.0965916499 | 1.581 | |
1 | 0.2445842508 | 0.0790825544 | 1.293 |
t | x | AE at α = 0.5 | AE at α = 0.75 | AE at α = 1 |
---|---|---|---|---|
0.2 | 0.0805629452 | 0.0502204062 | 0.0325020875 | |
0.4 | 0.0825454718 | 0.0515331039 | 0.0334241734 | |
0.1 | 0.6 | 0.0839111844 | 0.0524787587 | 0.0341170570 |
0.8 | 0.0846437383 | 0.0530448606 | 0.0345706478 | |
1 | 0.0847452771 | 0.0532295274 | 0.0347813764 | |
0.2 | 0.1386150391 | 0.1064055404 | 0.0816294703 | |
0.4 | 0.1421027846 | 0.1091805284 | 0.0838571430 | |
0.25 | 0.6 | 0.1445063572 | 0.1111623891 | 0.0855012205 |
0.8 | 0.1457962927 | 0.1123251454 | 0.0865387309 | |
1 | 0.1459764695 | 0.1126662559 | 0.0869633834 |
t | x | AE at α = 0.5 | AE at α = 0.75 | AE at α = 1 |
---|---|---|---|---|
0.2 | 0.0365409370 | 0.0162647517 | 0.0044485940 | |
0.4 | 0.0372349264 | 0.0167576585 | 0.0047433264 | |
0.1 | 0.6 | 0.0378161928 | 0.0172017544 | 0.0050225392 |
0.8 | 0.0382802895 | 0.0175933608 | 0.0052838629 | |
1 | 0.0386242276 | 0.0179294469 | 0.0055251728 | |
0.2 | 0.0493801887 | 0.0277102702 | 0.0109897476 | |
0.4 | 0.0502167121 | 0.0285674155 | 0.0116808654 | |
0.25 | 0.6 | 0.0508790642 | 0.0293301937 | 0.0123303104 |
0.8 | 0.0513628857 | 0.0299925619 | 0.0129326754 | |
1 | 0.0516662223 | 0.0305498127 | 0.0134832205 |
t | x | Numerical Simulation at | Numerical Simulation at | Numerical Simulation at |
---|---|---|---|---|
0.2 | 1.837707373 | 1.917052547 | 1.980814044 | |
0.4 | 1.625576979 | 1.975701657 | 2.036756119 | |
0.1 | 0.6 | 1.530086586 | 2.045377487 | 2.098530194 |
0.8 | 1.551236193 | 2.126080036 | 2.166136269 | |
1 | 1.689025800 | 2.217809305 | 2.239574344 | |
0.2 | 1.713577815 | 1.674859093 | 1.702150273 | |
0.4 | 1.553928691 | 1.670189950 | 1.748038242 | |
0.25 | 0.6 | 1.503958022 | 1.722897876 | 1.830376211 |
0.8 | 1.563665809 | 1.832982869 | 1.949164180 | |
1 | 1.733052051 | 2.000444931 | 2.104402148 |
t | x | Numerical Simulation at | Numerical Simulation at | Numerical Simulation at |
---|---|---|---|---|
0.2 | 1.459238898 | 1.424447874 | 1.321163456 | |
0.4 | 1.754369291 | 1.528622455 | 1.421371381 | |
0.1 | 0.6 | 1.932859684 | 1.605050337 | 1.515747306 |
0.8 | 1.994710077 | 1.653731523 | 1.604291231 | |
1 | 1.939920471 | 1.674666009 | 1.687003156 | |
0.2 | 1.324648176 | 1.528861254 | 1.499959102 | |
0.4 | 2.088050864 | 1.776106048 | 1.590008633 | |
0.25 | 0.6 | 2.559853552 | 1.913672387 | 1.643608164 |
0.8 | 2.740056238 | 1.941560270 | 1.660757695 | |
1 | 2.628658925 | 1.859769698 | 1.641457227 |
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Alderremy, A.A.; Shah, R.; Iqbal, N.; Aly, S.; Nonlaopon, K. Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series. Symmetry 2022, 14, 1944. https://doi.org/10.3390/sym14091944
Alderremy AA, Shah R, Iqbal N, Aly S, Nonlaopon K. Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series. Symmetry. 2022; 14(9):1944. https://doi.org/10.3390/sym14091944
Chicago/Turabian StyleAlderremy, Aisha Abdullah, Rasool Shah, Naveed Iqbal, Shaban Aly, and Kamsing Nonlaopon. 2022. "Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series" Symmetry 14, no. 9: 1944. https://doi.org/10.3390/sym14091944
APA StyleAlderremy, A. A., Shah, R., Iqbal, N., Aly, S., & Nonlaopon, K. (2022). Fractional Series Solution Construction for Nonlinear Fractional Reaction-Diffusion Brusselator Model Utilizing Laplace Residual Power Series. Symmetry, 14(9), 1944. https://doi.org/10.3390/sym14091944