Fourth-Kind Chebyshev Operational Tau Algorithm for Fractional Bagley-Torvik Equation

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.