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This paper proposes a numerical technique to solve the time-fractional generalized Kawahara differential equation (TFGKDE). Certain shifted Lucas polynomials are utilized as basis functions. We first establish some new formulas concerned with the introduced polynomials and then tackle the equation using a suitable collocation procedure. The integer and fractional derivatives of the shifted polynomials are used with the typical collocation method to convert the equation with its governing conditions into a system of algebraic equations. The convergence and error analysis of the proposed double expansion are rigorously investigated, demonstrating its accuracy and efficiency. Illustrative examples are provided to validate the effectiveness and applicability of the proposed algorithm.
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; Abdulrahman Khalid Al-Harbi 2 ; Omar Mazen Alqubori 2
; Alharbi, Mohammed H 2
; Ahmed Gamal Atta 3
1 Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt; Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia;
2 Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia;
3 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt;