Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations
| Autor: | Waleed M. Abd-Elhameed, José António Tenreiro Machado, Youssri H. Youssri |
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| Rok vydání: | 2021 |
| Předmět: |
Chebyshev polynomials
Applied Mathematics Computational Mechanics General Physics and Astronomy Statistical and Nonlinear Physics 010103 numerical & computational mathematics Delay differential equation 01 natural sciences Hypergeometric distribution Fractional calculus 010101 applied mathematics Mechanics of Materials Modeling and Simulation Applied mathematics 0101 mathematics Hypergeometric function Engineering (miscellaneous) Mathematics |
| Zdroj: | International Journal of Nonlinear Sciences and Numerical Simulation. 23:1253-1268 |
| ISSN: | 2191-0294 1565-1339 |
| DOI: | 10.1515/ijnsns-2020-0124 |
| Popis: | This paper presents an explicit formula that approximates the fractional derivatives of Chebyshev polynomials of the first-kind in the Caputo sense. The new expression is given in terms of a terminating hypergeometric function of the type 4 F 3(1). The integer derivatives of Chebyshev polynomials of the first-kind are deduced as a special case of the fractional ones. The formula will be applied for obtaining a spectral solution of a certain type of fractional delay differential equations with the aid of an explicit Chebyshev tau method. The shifted Chebyshev polynomials of the first-kind are selected as basis functions and the spectral tau method is employed for obtaining the desired approximate solutions. The convergence and error analysis are discussed. Numerical results are presented illustrating the efficiency and accuracy of the proposed algorithm. |
| Databáze: | OpenAIRE |
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