Numerical solution method for multi-term variable order fractional differential equations by shifted Chebyshev polynomials of the third kind
| Autor: | Arzu Turan Dincel, Sadiye Nergis Tural-Polat |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Chebyshev polynomials
Operational matrix method Variable-order fractional differential equations General Engineering Order (ring theory) Shifted Chebyshev polynomials of the third kind Term (logic) Multi-term fractional differential equations Engineering (General). Civil engineering (General) Algebraic equation Error analysis Applied mathematics TA1-2040 Fractional differential Mathematics Variable (mathematics) |
| Zdroj: | Alexandria Engineering Journal, Vol 61, Iss 7, Pp 5145-5153 (2022) |
| ISSN: | 1110-0168 |
| Popis: | Multi-term variable-order fractional differential equations (VO-FDEs) are considered to be one of the tools to illustrate the behavior of transient-regime real-life phenomena precisely. The analytical solutions of VO-FDEs are generally very hard to obtain. Therefore, in this study, an approximation method for the solution of multi-term VO-FDEs is proposed using shifted Chebyshev polynomials of the third kind (SCP3). The method employs the operational matrices of SCP3 to proximate the VO-FDEs with a system of algebraic equations. The solution of which also yields the approximate result for the multi-term VO-FDE. An error analysis is also included. The SCP3 method is examined on several examples demonstrating the precision and prowess of the method. |
| Databáze: | OpenAIRE |
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