Geodesic
Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 6, p. 981 .

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In this paper, the shifted Gegenbauer-Gauss collocation (SGGC) me\-thod 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.
Classification : 34K40, 65N35, 33C45
Keywords: Neutral fractional functional-differential equations, proportional delay, collocation method, shifted Gegenbauer-Gauss quadrature, shifted Gegenbauer polynomials 
@article{KJM_2022_46_6_a11,
     author = {R. M. Hafez and Y. H. Youssri},
     title = {Shifted {Gegenbauer-Gauss} {Collocation} {Method} for {Solving} {Fractional} {Neutral} {Functional-Differential} {Equations} with {Proportional} {Delays}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {981 },
     publisher = {mathdoc},
     volume = {46},
     number = {6},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2022_46_6_a11/}
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R. M. Hafez; Y. H. Youssri. Shifted Gegenbauer-Gauss Collocation Method for Solving Fractional Neutral Functional-Differential Equations with Proportional Delays. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 6, p. 981 . http://geodesic.mathdoc.fr/item/KJM_2022_46_6_a11/