Generalized Legendre Polynomial Configuration Method for Solving Numerical Solutions of Fractional Pantograph Delay Differential Equations
Abstract - 86
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Keywords

Caputo fractional derivatives
Generalized legendre polynomial
Delay fractional differential equations

How to Cite

Cui, X., Feng, Y., & Jiang, J. (2023). Generalized Legendre Polynomial Configuration Method for Solving Numerical Solutions of Fractional Pantograph Delay Differential Equations. Journal of Advances in Applied & Computational Mathematics, 10, 88–101. https://doi.org/10.15377/2409-5761.2023.10.9

Abstract

This paper develops a numerical approach for solving fractional pantograph delay differential equations using generalized Legendre polynomials. These polynomials are derived from generalized Taylor bases, which facilitate the approximation of the underlying analytical solutions, leading to the formulation of numerical solutions. The fractional pantograph delay differential equation is then transformed into a finite set of nonlinear algebraic equations using collocation points. Following this step, Newton's iterative method is applied to the resultant set of nonlinear algebraic equations to compute their numerical solutions. An error analysis for this methodology is subsequently presented, accompanied by numerical examples demonstrating its accuracy and efficiency. Overall, this study contributes a more streamlined and productive tool for determining the numerical solution of fractional differential equations.

https://doi.org/10.15377/2409-5761.2023.10.9
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Copyright (c) 2023 Xueying Cui, Yuqiang Feng, Jun Jiang