Novel approach by shifted Schröder polynomials for solving the fractional Bagley-Torvik equation

Abstract

Abstract This work is dedicated to proposing a spectral tau solution for the fractional Bagley-Torvik equation (FBTE). The suggested solution is stated as a sum of basis functions, which are selected to be the Schr <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mover accent="true"> <mml:mrow> <mml:mi>o</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>̈</mml:mo> </mml:mrow> </mml:mover> </mml:math> der polynomials (SPs). By applying the proposed spectral tau approach, we derive a system of linear equations, and we solve it approximately by applying the Gauss elimination method. The error analysis is analyzed in detail. Additionally, numerical comparisons with other methods found in the literature are conducted. The numerical results validate the suggested method's accuracy, computational efficiency, and ease of use.