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Numerical solutions of generalized fractional pantograph equations with variable coefficients using shifted Chebyshev polynomials

Abstract : In this paper, an efficient numerical technique based on the shifted Chebyshev polynomials (SCPs) is established to obtain numerical solutions of generalized fractional pantograph equations with variable coefficients. These polynomials are orthogonal and have compact support on [0, L]. We use these polynomi-als to approximate the unknown function. Using the properties of the SCPs, we derive the generalized pantograph operational matrix of SCPs and the one of fractional-order differentiation. Then the original problems can be transformed to a system of algebraic equations based on these matrices. By solving these algebraic equations, we can obtain numerical solutions. In addition, we investigate the error analysis and introduce the process of error correction for improving the precision of numerical solutions. Lastly, by giving some examples and comparing with other existing methods, the validity and efficiency of our method is demonstrated.
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Submitted on : Tuesday, May 4, 2021 - 3:30:20 PM
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Li-Ping Wang, Yi-Ming Chen, Da-Yan Liu, Driss Boutat. Numerical solutions of generalized fractional pantograph equations with variable coefficients using shifted Chebyshev polynomials. International Journal of Computer Mathematics, Taylor & Francis, 2019, 96 (12), pp.2487-2510. ⟨10.1080/00207160.2019.1573992⟩. ⟨hal-02884254⟩

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