A Computational Scheme Based on Fractional Basis Functions For Solving Fractional Bagley–Torvik Equation

This study aims to present a spectral collocation approach for treating fractional Bagley–Torvik equations using fractional basis functions. The Bagley–Torvik equation is critically important in a wide range of applied scientific and engineering disciplines. The fractional form of the Bagley–Torvik equations enables the modeling of complex systems with memory-dependent or nonlocal dynamics. To solve the fractional Bagley–Torvik equation, we propose a collocation method based on Jaiswal polynomials. We initially introduce the Jaiswal polynomials to accomplish this purpose. We then determine their fractional analogs by applying a transformation. After that, by computing the operational matrix of fractional Jaiswal functions, we approximate the fractional and ordinary derivatives of the main equation. The numerical method leads to a linear system of equations that can be solved by various numerical methods. In addition, we prove that the numerical scheme is convergent, and we obtain an error bound for the remainder term of our numerical scheme. Finally, several numerical simulations are used to highlight the method’s functioning.