Abstract and Applied Analysis

Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems

D. Baleanu, A. H. Bhrawy, and T. M. Taha

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Abstract

We present a direct solution technique for approximating linear multiterm fractional differential equations (FDEs) on semi-infinite interval, using generalized Laguerre polynomials. We derive the operational matrix of Caputo fractional derivative of the generalized Laguerre polynomials which is applied together with generalized Laguerre tau approximation for implementing a spectral solution of linear multiterm FDEs on semi-infinite interval subject to initial conditions. The generalized Laguerre pseudo-spectral approximation based on the generalized Laguerre operational matrix is investigated to reduce the nonlinear multiterm FDEs and its initial conditions to nonlinear algebraic system, thus greatly simplifying the problem. Through several numerical examples, we confirm the accuracy and performance of the proposed spectral algorithms. Indeed, the methods yield accurate results, and the exact solutions are achieved for some tested problems.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 546502, 10 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450266

Digital Object Identifier
doi:10.1155/2013/546502

Mathematical Reviews number (MathSciNet)
MR3066294

Zentralblatt MATH identifier
1291.65240

Citation

Baleanu, D.; Bhrawy, A. H.; Taha, T. M. Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 546502, 10 pages. doi:10.1155/2013/546502. https://projecteuclid.org/euclid.aaa/1393450266


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