Legendre Least Squares Approach with Perturbation for the Solution of Fractional Order Differential Equations - Uwaheren, Ohigweren Airenoni1; Ogunlaran, Esther Olakemi; Omoniyi, Temitope Rebecca (FUDMA Journal of Sciences, 2026)
In this article, we present the Perturbed Shifted Legendre based approach for the solution of fractional order differential equations using Least Squares Method.  Here, an assumed solution is substituted into the slightly perturbed fractional order differential equation and the residual equation is minimized to yield a system of equations which are then solved to obtain the constants involved.  The required approximate solution is obtained when the constant values are substituted into the assumed solution.
Keywords: Fractional Calculus; Least Squares Method; Legendre Polynomial; Fractional Differential Equation; Basis Function