Numerical Solution of Fractional Order Differential Equations by Chebyshev Least Squares Approximation Method

In this paper, fractional differential equations (FDEs) are solved numerically using the least squares method (LSM). Shifted Chebyshev polynomials are used as the basis functions, and the results are compared with the exact solutions. Several numerical examples are presented to illustrate the theoretical results and are also compared with the outcomes obtained from other numerical methods. It is found that the results of the proposed approximate method converge rapidly to the exact solutions.