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

Abstract

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.

Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays

“…The absolute errors in the given tables are the values of |u(x) − u N (x)| at selected points. Example 6.1 ( [7]). Consider the following fractional neutral functional-differential equation with proportional delay…”

“…In Table 1, we list the absolute errors obtained by the shifted Gegenbauer-Gauss collocation method, with different values of α at N = 22. The outcomes are contrasted with the outcome of the modifed generalized Laguerre-Gauss collocation (MGLC) method [7]. It is clear from this table that, the solutions got by our technique are superior in examination with modifed generalized Laguerre-Gauss collocation scheme [7].…”

A Computational Technique for Solving Singularly Perturbed Delay Partial Differential Equations

“…The method also can be extended on different type of mathematical models but some mod-230 B. Gürbüz ifications are required [40], [27], [28], [22], [25], [5].…”

On the numerical solution of space fractional order diffusion equation via shifted Chebyshev polynomials of the third kind

“…It does indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables (see for instance, Boyd (2001), Bhrawy et al (2013Bhrawy et al ( , 2014a, Kilbas et al (2006), Miller and Ross (1993), Oldham and Spanier (1974), Podlubny (1999), Rossikhin and Shitikova (1997)). …”