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The Numerical Approximation of Caputo Fractional Derivative of Higher Orders Using A Shifted Gegenbauer Pseudospectral Method: Two-Point Boundary Value Problems of the Bagley Torvik Type Case Study
This work introduces a novel framework for approximating Caputo fractional derivatives (FDs) of orders greater than one using a shifted Gegenbauer pseudospectral (SGPS) method. Unlike traditional approaches, our method employs a strategic change of variables to transform the Caputo FD into a scaled integral of the mth-derivative of the Lagrange …