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Spectral approximations to the fractional integral and derivative

✍ Scribed by Changpin Li, Fanhai Zeng, Fawang Liu

Book ID
115064269
Publisher
SP Versita
Year
2012
Tongue
English
Weight
486 KB
Volume
15
Category
Article
ISSN
1311-0454

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✦ Synopsis

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

πŸ“œ SIMILAR VOLUMES

The fractional quantum derivative and it
The fractional quantum derivative and its integral representations
✍ Manuel Duarte Ortigueira πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 183 KB

The quantum fractional derivative is defined using formulations analogue to the common GrΓΌnwald-Letnikov derivatives. While these use a linear variable scale, the quantum derivative uses an exponential scale and is defined in R + or R Γ€ . Two integral formulations similar to the usual Liouville deri