Fourth-Kind Chebyshev Operational Tau Algorithm for Fractional Bagley-Torvik Equation | ||
| Frontiers in Scientific Research and Technology | ||
| Volume 11, Issue 1, August 2025 PDF (497.12 K) | ||
| Document Type: Original Article | ||
| DOI: 10.21608/fsrt.2025.358327.1152 | ||
| Authors | ||
| Mohamed Ramadan Zeen El Deen* 1; Youssri Hassan Youssri2; Mostafa Ahmed Taema3 | ||
| 1Department of Mathematics, Faculty of Science, Suez University, Suez, Egypt | ||
| 2Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt | ||
| 3Faculty of Engineering, King Salman International University, El-Tur, Egypt | ||
| Abstract | ||
| In this work, a new numerical method for solving the Fractional Bagley-Torvik problem is established. The fundamental idea behind this novel approach is the clever incorporation of fourth-kind Chebyshev polynomials into the well-known operational tau technique.This study's main goal is to improve the accuracy and efficiency of the Fractional Bagley-Torvik equation solution. Managing non-homogeneous boundary conditions effectively is a crucial breakthrough that makes this possible. It is possible to transform these non-homogeneous situations into a more controllable and tractable homogenous form by using a methodical transformation process. This transformation phase enhances the numerical method's overall accuracy and efficiency while greatly streamlining the solution procedure. The study includes a number of carefully chosen numerical examples to confirm the effectiveness and usefulness of this suggested method. The accuracy and resilience of the Chebyshev polynomial-based operational tau approach in handling the intricacies of the Fractional Bagley-Torvik equation are demonstrated by these actual examples. By using these examples, the study hopes to demonstrate convincingly that this new approach provides a workable and efficient way to solve this difficult class of differential equations. | ||
| Keywords | ||
| Chebyshev polynomial; Fractional Bagley-Torvik equation; Fractional differential equations; spectral method | ||
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