Solving Time-Fractional Partial Differential Equation Using Chebyshev Cardinal Functions
Abstract
:1. Introduction
2. Chebyshev Cardinal Functions
2.1. Operational Matrix of Derivation
- 1.
- If , due to the fact that , we have
- 2.
- If , according to Equation (14), we get
2.2. Operational Matrix of Fractional Integration
2.3. Operational Matrix of Fractional Derivation
3. Galerkin Method
Convergence Analysis
4. Numerical Experiments
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
TFPDEs | Time-fractional partial differential equations |
CCFs | Chebyshev cardinal functions |
RBFs | Radial basis functions |
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RBFs method (m = 51) | ||||
CCFs method (m = 3) | ||||
RBFs method (m = 121) | ||||
CCFs method (m = 9) | ||||
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Bin Jebreen, H.; Cattani, C. Solving Time-Fractional Partial Differential Equation Using Chebyshev Cardinal Functions. Axioms 2022, 11, 642. https://doi.org/10.3390/axioms11110642
Bin Jebreen H, Cattani C. Solving Time-Fractional Partial Differential Equation Using Chebyshev Cardinal Functions. Axioms. 2022; 11(11):642. https://doi.org/10.3390/axioms11110642
Chicago/Turabian StyleBin Jebreen, Haifa, and Carlo Cattani. 2022. "Solving Time-Fractional Partial Differential Equation Using Chebyshev Cardinal Functions" Axioms 11, no. 11: 642. https://doi.org/10.3390/axioms11110642