Numerical Solution for Solving Linear Fractional Differential Equations using Chebyshev Wavelets

In this paper, a numerical method for solving linear fractional differential equations using Chebyshev wavelets matrices has been presented. Fractional differential equations have received great attention in the recent period due to the expansion of their uses in many applications, It is difficult to find a solution to them by the analytical method due to the presence of derivatives with fractional orders. Therefore, we resort to numerical solutions. The use of wavelets in solving these equations is a relatively new method, as it was found to give more accurate results than other methods. We created Chebyshev matrices by utilizing Chebyshev sequences, where these matrices can be created in different sizes, and the larger the matrix size, The results are more accurate. Chebyshev wavelet matrices are characterized by their speed when compared to other wavelet matrices. The algorithm converts fractional differential equations into algebraic equations by using the derivative of an operational matrix of the pulsing mass of the fractional integral with Chebyshev matrices. Then, the solution is found by applying the algorithm and comparing it with the exact solution. The results are convergent with very small errors. To prove the effectiveness and applicability of the algorithm, for validation, and show how the results are close to the exact solution, several examples have been solved.