| Spectral Solution for Solving Fractional Differential Equations Using Generalized Fibonacci Polynomials |
| Paper ID : 1048-ISCHU |
| Authors |
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Sara Mohamed * Mathematics department, Faculty of Science, Helwan University, Cairo, Egypt |
| Abstract |
| The research paper introduces a numerical method that provides an approximate solution to the Bagley-Torvik equation. The key idea of the algorithm is to utilize the Fibonacci polynomials as a basis function. This method depends on using the operational matrix of the fractional derivative of the Fibonacci polynomials to solve the fractional Bagley-Torvik equation with the aid of the tau spectral method. The algorithm's fundamental approach is based on transforming the Bagley-Torvik equation with its initial (boundary) conditions into an algebraic system of equations. The study includes an extensive investigation of the convergence and error analysis of the generalized Fibonacci expansion. To showcase the algorithm's effectiveness and applicability, several numerical examples are presented. These examples serve to illustrate the successful implementation of the method for solving the Bagley-Torvik equation. Overall, the research paper provides valuable insights into a numerical method that offers an approximate solution for the Bagley-Torvik equation, demonstrating its potential usefulness in practical applications. |
| Keywords |
| Bagley-Torvik equation; Generalized Fibonacci Polynomials; Tau Method |
| Status: Abstract Accepted (Poster Presentation) |