Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems
Abstract
:1. Introduction
2. Preliminaries
2.1. The Variable-Order Fractional Calculus
2.2. Bernoulli Polynomials
3. Operational Matrix of Variable-Order Fractional Integration
4. Methods of Solution
4.1. Approach I
4.2. Approach II
5. Error Bounds
6. Test Problems
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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M | 1 | 2 | 3 | 2 | 5 |
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J |
Method | ||||
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Approach I | ||||
Approach II |
M | 1 | 3 | 5 | 7 |
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J |
M | 2 | 4 | 6 | 8 |
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J |
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Nemati, S.; Torres, D.F.M. Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems. Axioms 2020, 9, 114. https://doi.org/10.3390/axioms9040114
Nemati S, Torres DFM. Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems. Axioms. 2020; 9(4):114. https://doi.org/10.3390/axioms9040114
Chicago/Turabian StyleNemati, Somayeh, and Delfim F. M. Torres. 2020. "Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control-Affine Problems" Axioms 9, no. 4: 114. https://doi.org/10.3390/axioms9040114