An Efficient Analytical Approach to Investigate Fractional Caudrey–Dodd–Gibbon Equations with Non-Singular Kernel Derivatives
Abstract
:1. Introduction
2. Preliminaries
3. Methodology
3.1. Case I
3.2. Case II
4. Convergence Analysis
5. Applications
- Solution in Terms of
- Solution in Terms of
- Solution in Terms of
- Solution in Terms of
6. Numerical Simulation Studies
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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0.2 | 0.81468 | 0.80893 | 0.80375 | 0.80317 | 0.80317 | |
0.4 | 0.71790 | 0.70803 | 0.69916 | 0.69818 | 0.69818 | |
0.01 | 0.6 | 0.57747 | 0.56588 | 0.55545 | 0.55429 | 0.55429 |
0.8 | 0.42425 | 0.41299 | 0.40286 | 0.40173 | 0.40173 | |
1 | 0.28190 | 0.27220 | 0.26347 | 0.26250 | 0.26250 | |
0.2 | 0.81531 | 0.80953 | 0.80432 | 0.80374 | 0.80374 | |
0.4 | 0.71898 | 0.70906 | 0.70015 | 0.69915 | 0.69915 | |
0.02 | 0.6 | 0.57874 | 0.56708 | 0.55660 | 0.55544 | 0.55544 |
0.8 | 0.42548 | 0.41416 | 0.40398 | 0.40285 | 0.40285 | |
1 | 0.28296 | 0.27321 | 0.26444 | 0.26346 | 0.26346 | |
0.2 | 0.81593 | 0.81012 | 0.80490 | 0.80430 | 0.80430 | |
0.4 | 0.72004 | 0.71009 | 0.70113 | 0.70013 | 0.70013 | |
0.03 | 0.6 | 0.57999 | 0.56829 | 0.55776 | 0.55659 | 0.55659 |
0.8 | 0.42670 | 0.41533 | 0.40511 | 0.40397 | 0.40397 | |
1 | 0.28401 | 0.27421 | 0.26540 | 0.26443 | 0.26443 | |
0.2 | 0.81655 | 0.81072 | 0.80547 | 0.80486 | 0.80486 | |
0.4 | 0.72111 | 0.71111 | 0.70211 | 0.70110 | 0.70110 | |
0.04 | 0.6 | 0.58124 | 0.56949 | 0.55892 | 0.55774 | 0.55774 |
0.8 | 0.42792 | 0.41650 | 0.40623 | 0.40509 | 0.40509 | |
1 | 0.28506 | 0.27522 | 0.26637 | 0.26540 | 0.26540 | |
0.2 | 0.81717 | 0.81131 | 0.80604 | 0.80541 | 0.80541 | |
0.4 | 0.72216 | 0.71212 | 0.70310 | 0.70207 | 0.70207 | |
0.05 | 0.6 | 0.58248 | 0.57068 | 0.56007 | 0.55889 | 0.55889 |
0.8 | 0.42912 | 0.41766 | 0.40735 | 0.40622 | 0.40622 | |
1 | 0.28610 | 0.27622 | 0.26734 | 0.26637 | 0.26637 |
0.00 | 0.0000000000 | 0.0000000000 | |
0.01 | 0.0000351211 | 6.6361100000 | |
0.5 | 0.02 | 0.0002810211 | 7.7452360000 |
0.03 | 0.0009486029 | 1.3820520000 | |
0.04 | 0.0022488807 | 1.1712320000 | |
0.05 | 0.0043929376 | 1.8875059000 | |
0.00 | 0.0000000000 | 0.0000000000 | |
0.01 | 0.0000141429 | 7.0112118000 | |
1.0 | 0.02 | 0.0001130449 | 2.7878834000 |
0.03 | 0.0003811928 | 1.2331435000 | |
0.04 | 0.0009027666 | 1.1006695700 | |
0.05 | 0.0017616292 | 1.0116290000 |
0.2 | 0.01 | 1.08932 | 1.02820 | 0.96711 |
0.4 | 1.07550 | 0.97075 | 0.86604 | |
0.6 | 0.97003 | 0.84689 | 0.72380 | |
0.8 | 0.81012 | 0.69050 | 0.57093 | |
1 | 0.63629 | 0.53322 | 0.43020 | |
0.2 | 0.02 | 1.09602 | 1.03458 | 0.97318 |
0.4 | 1.08698 | 0.98168 | 0.87644 | |
0.6 | 0.98352 | 0.85974 | 0.73603 | |
0.8 | 0.82323 | 0.70298 | 0.58281 | |
1 | 0.64758 | 0.54398 | 0.44044 | |
0.2 | 0.03 | 1.10265 | 1.04092 | 0.97925 |
0.4 | 1.09834 | 0.99255 | 0.88684 | |
0.6 | 0.99687 | 0.87252 | 0.74826 | |
0.8 | 0.83620 | 0.71539 | 0.59469 | |
1 | 0.65875 | 0.55467 | 0.45067 | |
0.2 | 0.04 | 1.10923 | 1.04725 | 0.98532 |
0.4 | 1.10962 | 1.00338 | 0.89725 | |
0.6 | 1.01013 | 0.88525 | 0.76049 | |
0.8 | 0.84908 | 0.72777 | 0.60657 | |
1 | 0.66985 | 0.56533 | 0.46091 | |
0.2 | 0.05 | 1.11578 | 1.05355 | 0.99139 |
0.4 | 1.12084 | 1.01419 | 0.90765 | |
0.6 | 1.02333 | 0.89796 | 0.77272 | |
0.8 | 0.86190 | 0.74011 | 0.61845 | |
1 | 0.68090 | 0.57597 | 0.47115 |
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Fathima, D.; Alahmadi, R.A.; Khan, A.; Akhter, A.; Ganie, A.H. An Efficient Analytical Approach to Investigate Fractional Caudrey–Dodd–Gibbon Equations with Non-Singular Kernel Derivatives. Symmetry 2023, 15, 850. https://doi.org/10.3390/sym15040850
Fathima D, Alahmadi RA, Khan A, Akhter A, Ganie AH. An Efficient Analytical Approach to Investigate Fractional Caudrey–Dodd–Gibbon Equations with Non-Singular Kernel Derivatives. Symmetry. 2023; 15(4):850. https://doi.org/10.3390/sym15040850
Chicago/Turabian StyleFathima, Dowlath, Reham A. Alahmadi, Adnan Khan, Afroza Akhter, and Abdul Hamid Ganie. 2023. "An Efficient Analytical Approach to Investigate Fractional Caudrey–Dodd–Gibbon Equations with Non-Singular Kernel Derivatives" Symmetry 15, no. 4: 850. https://doi.org/10.3390/sym15040850
APA StyleFathima, D., Alahmadi, R. A., Khan, A., Akhter, A., & Ganie, A. H. (2023). An Efficient Analytical Approach to Investigate Fractional Caudrey–Dodd–Gibbon Equations with Non-Singular Kernel Derivatives. Symmetry, 15(4), 850. https://doi.org/10.3390/sym15040850