Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays
Ramy M. Hafez, Y. H. Youssri
Abstract
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.
Topics & Concepts
MathematicsGaussOrthogonal collocationCollocation methodMathematical analysisQuadrature (astronomy)Algebraic equationGaussian quadratureCollocation (remote sensing)Gegenbauer polynomialsApplied mathematicsDifferential equationOrthogonal polynomialsNyström methodIntegral equationClassical orthogonal polynomialsPhysicsNonlinear systemOrdinary differential equationOpticsRemote sensingGeologyQuantum mechanicsFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods in engineering