Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule
Abstract
:1. Introduction
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- Good accuracy and simple implementation.
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- Exponential convergence.
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- Provide a global approach in
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- Provide the possibility of error analysis and convergence of method due to the clear and strong theoretical structure.
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- It can be a basis for solving problems with higher complexity.
2. Laplace Transform Method and Quadrature Rule
3. Special Cases and Their Examples
3.1. First Order FDE
3.2. FDE with Delay Term
3.3. Second Order FDE
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Soradi-Zeid, S.; Mesrizadeh, M.; Cattani, C. Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule. Fractal Fract. 2021, 5, 111. https://doi.org/10.3390/fractalfract5030111
Soradi-Zeid S, Mesrizadeh M, Cattani C. Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule. Fractal and Fractional. 2021; 5(3):111. https://doi.org/10.3390/fractalfract5030111
Chicago/Turabian StyleSoradi-Zeid, Samaneh, Mehdi Mesrizadeh, and Carlo Cattani. 2021. "Numerical Solutions of Fractional Differential Equations by Using Laplace Transformation Method and Quadrature Rule" Fractal and Fractional 5, no. 3: 111. https://doi.org/10.3390/fractalfract5030111