Numerical Investigation of Fredholm Fractional Integro-differential Equations by Least Squares Method and Compact Combination of Shifted Chebyshev Polynomials

Abstract

In this study, linear Fredholm fractional integro-differential equations (FIDEs) are numerically solved, where the fractional derivative is considered in the Caputo sense. In this work, the least squares method (LSM) using a compact combination of shifted Chebyshev polynomials (SCP) of the first Kind is applied to solving a class of FIDEs. Our aim is to write the unknown function as a series of a linear combination of SCP, and then to reduce the problem to a system of linear algebraic equations, which will be solved for the unknown constants associated with the approximate solution, using MATLAB R2020a. Finally, numerical examples are presented to confirm the reliability, applicability, and efficiency of this method, in addition, various comparisons are also shown.

Utilizing Cubic B-Spline Collocation Technique for Solving Linear and Nonlinear Fractional Integro-Differential Equations of Volterra and Fredholm Types

“…Cubic Bsplines, known for their flexibility and smoothness properties, offer an excellent framework for approximating functions involving fractional derivatives. Benzahi et al [1] delved into the numerical investigation of Fredholm FIDEs using the least squares method combined with a compact combination of shifted Chebyshev polynomials. This method, involving a series expansion in terms of Chebyshev polynomials, provides high accuracy, particularly in bounded domains.…”