scholarly journals A Shifted Jacobi-Gauss Collocation Scheme for Solving Fractional Neutral Functional-Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
A. H. Bhrawy ◽  
M. A. Alghamdi
Keyword(s):  
Differential Equations ◽  
Jacobi Polynomials ◽  
Functional Differential Equations ◽  
Numerical Results ◽  
Algebraic Equations ◽  
Integration Technique ◽  
Neutral Functional Differential Equations ◽  
Shifted Jacobi Polynomials ◽  
Collocation Scheme ◽  
Functional Differential

The shifted Jacobi-Gauss collocation (SJGC) scheme is proposed and implemented to solve the fractional neutral functional-differential equations with proportional delays. The technique we have proposed is based upon shifted Jacobi polynomials with the Gauss quadrature integration technique. The main advantage of the shifted Jacobi-Gauss scheme is to reduce solving the generalized fractional neutral functional-differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi-Gauss collocation nodes. Numerical results demonstrate the accuracy, and versatility of the proposed algorithm.

scholarly journals A Modified Generalized Laguerre-Gauss Collocation Method for Fractional Neutral Functional-Differential Equations on the Half-Line

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ali H. Bhrawy ◽  
Abdulrahim AlZahrani ◽  
Dumitru Baleanu ◽  
Yahia Alhamed
Keyword(s):  
Differential Equations ◽  
Laguerre Polynomials ◽  
Functional Differential Equations ◽  
Numerical Results ◽  
Half Line ◽  
Algebraic Equations ◽  
Neutral Functional Differential Equations ◽  
Generalized Laguerre Polynomials ◽  
Collocation Points ◽  
Functional Differential

The modified generalized Laguerre-Gauss collocation (MGLC) method is applied to obtain an approximate solution of fractional neutral functional-differential equations with proportional delays on the half-line. The proposed technique is based on modified generalized Laguerre polynomials and Gauss quadrature integration of such polynomials. The main advantage of the present method is to reduce the solution of fractional neutral functional-differential equations into a system of algebraic equations. Reasonable numerical results are achieved by choosing few modified generalized Laguerre-Gauss collocation points. Numerical results demonstrate the accuracy, efficiency, and versatility of the proposed method on the half-line.

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