Solutions of the Generalized Abel’s Integral Equation using Laguerre Orthogonal Approximation

In this paper, a numerical approximation is drafted for solving the generalized Abel’s integral equation by practicing Laguerre orthogonal polynomials. The proposed approximation is framed for the first and second kinds of the generalized Abel’s integral equation. We have utilized the properties of fractional order operators to interpret Abel’s integral equation as a fractional integral equation. It offers a new approach by employing Laguerre polynomials to approximate the integrand of a fractional integral equation. Given examples demonstrate the simplicity and suitability of the method. The graphical representation of exact and approximate solutions helps in visualizing a solution at discrete points, together with the absolute error function. We have also carried out a numerical comparison with Chebyshev polynomials to display less error in the posed formulation