Quantum mechanics

Gaussian quadrature

Differential equation

Classical orthogonal polynomials

Applied mathematics

Geology

Collocation method

Algebraic equation

Physics

Nonlinear system

Nyström method

Collocation (remote sensing)

Mathematics

Optics

Quadrature (astronomy)

Orthogonal collocation

Mathematical analysis

Gauss

Remote sensing

Ordinary differential equation

Gegenbauer polynomials

Integral equation

Orthogonal polynomials

Kragujevac Journal of Mathematics

In this paper, the shifted Gegenbauer-Gauss collocation (SGGC) method is applied to fractional neutral functional-diﬀerential equations with proportional delays. The technique we have used is based on shifted Gegenbauer polynomials and Gauss quadrature integration. The shifted Gegenbauer-Gauss method reduces solving the generalized fractional pantograph equation fractional neutral functional-diﬀerential equations to a system of algebraic equations. Reasonable numerical results are obtained by selecting few shifted Gegenbauer-Gauss collocation points. Numerical results demonstrate its accuracy, and versatility of the proposed techniques.

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