Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations
Abstract
:1. Introduction and Preliminaries
2. Preliminary
2.1. Fractional Calculus
2.2. The ADM and FPSM
3. Applying the ADM and FPSM for Specific
3.1. Case 1:
3.2. Case 2:
3.3. Case 3:
3.4. Case 4:
4. Test Examples
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. The First Six Expressions of Υ i for Case 1
Appendix B. The First Six Expressions of Υ i for Case 2
Appendix C. The First Six Expressions of Υ i for Case 3
Appendix D. The First Six Expressions of Υ i for Case 4
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ADM () | FPSM | Absolute Error | |
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ADM () | FPSM | Absolute Error | |
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ADM () | FPSM | Absolute Error | |
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ADM () | FPSM | Absolute Error | |
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Mohammed, P.O.; Machado, J.A.T.; Guirao, J.L.G.; Agarwal, R.P. Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations. Mathematics 2021, 9, 1070. https://doi.org/10.3390/math9091070
Mohammed PO, Machado JAT, Guirao JLG, Agarwal RP. Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations. Mathematics. 2021; 9(9):1070. https://doi.org/10.3390/math9091070
Chicago/Turabian StyleMohammed, Pshtiwan Othman, José António Tenreiro Machado, Juan L. G. Guirao, and Ravi P. Agarwal. 2021. "Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations" Mathematics 9, no. 9: 1070. https://doi.org/10.3390/math9091070