Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials
By A. A. El-Sayed, Praveen Agarwal. Mathematical methods in the applied sciences, 2019
109 citations recorded by the source corpus.
In this paper, shifted Legendre polynomials will be used for constructing the numerical solution for a class of multiterm variable‐order fractional differential equations. In the proposed method, the shifted Legendre operational matrix of the fractional variable‐order derivatives will be investigated. The fundamental problem is reduced to an algebraic system of equations using the constructed matrix and the collocation technique, which can be solved numerically. The error estimate of the proposed method is investigated. Some numerical examples are presented to prove the applicability, generality, and accuracy of the suggested method.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/ef86bc9463b97f294310afd62cc8da9bcbe32c52
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In Applied Mathematics
- Dumitru Băleanu
- Praveen Agarwal
- A. A. El-Sayed
- Thabet Abdeljawad
- Arran Fernandez
- Fahd Jarad
- Hari M. Srivastava
- Xiao-jun Yang
In Modeling and Simulation
- Praveen Agarwal
- Dumitru Băleanu
- A. A. El-Sayed
- Thabet Abdeljawad
- Arran Fernandez
- Amin Jajarmi
- Mehmet Yavuz
- Pshtiwan Othman Mohammed
In Numerical Analysis
- Dumitru Băleanu
- Praveen Agarwal
- A. A. El-Sayed
- Arran Fernandez
- Thabet Abdeljawad
- Pshtiwan Othman Mohammed
- Mehmet Yavuz
- Amin Jajarmi
Citations in the corpus
- A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations (2020, methodology): “This implies that we can obtain the error bound in case of using the shifted Legendre polynomials [50].”