Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems

被引:50
作者
Baleanu, D. [1 ,2 ,3 ]
Bhrawy, A. H. [4 ,5 ]
Taha, T. M. [5 ]
机构
[1] Cankaya Univ, Fac Arts & Sci, Dept Math & Comp Sci, TR-06810 Ankara, Turkey
[2] King Abdulaziz Univ, Fac Engn, Dept Chem & Mat Engn, Jeddah 21413, Saudi Arabia
[3] Inst Space Sci, Magurele, Romania
[4] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah, Saudi Arabia
[5] Beni Suef Univ, Fac Sci, Dept Math, Bani Suwayf, Egypt
关键词
DIFFERENTIAL-EQUATIONS; OPERATIONAL MATRIX; NUMERICAL-SOLUTION;
D O I
10.1155/2013/546502
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 multitermFDEs 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.
引用
收藏
页数:10
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