Generalized Lucas Polynomial Sequence Treatment of Fractional Pantograph Differential Equation

Paper ID : 1031-ISCHU

Authors

Shahenda Mohamed Sayed *1, Youssri Hassan Youssri2, Waleed Mohamed Abd-Elhameed2, Amany Saad Mohamed1 1Helwan University 2Cairo University

Abstract

This paper deals with the implementation and presentation of semi-analytic solutions of fractional pantograph differential equations (FPDEs) using generalized Lucas polynomials (GLPs). The derivation of our proposed algorithms is built on introducing an operational matrix of derivatives (OMDs) of the generalized Lucas polynomials and after that employing it to convert the problem into an algebraic system of equations whose solution can be found through some suitable algorithms such as Gauss elimination and Newton–Raphson methods. The convergence analysis of the generalized Lucas polynomials is deeply discussed by establishing some inequalities concerned with these polynomials. We point out that the Mathematica program was used to validate all the theoretical relationships in this paper, and we also point out that the numerical results obtained in this paper show that the proposed algorithms are effective and accurate. Finally, by providing various illustrative examples, including comparisons with the results obtained by some other existing literature methods, the efficiency and applicability of our proposed algorithms are demonstrated.

Keywords

Fractional differential equations · generalized Lucas polynomials · fractional pantograph differential equations · spectral methods · operational matrix · convergence analysis

Status: Abstract Accepted (Poster Presentation)