The Polynomial Least Squares Method for Nonlinear Fractional Volterra and Fredholm Integro-Differential Equations

Abstract

We present a relatively new and very efficient method to find approximate analytical solutions for a very general class of nonlinear fractional Volterra and Fredholm integro-differential equations. The test problems included and the comparison with previous results by other methods clearly illustrate the simplicity and accuracy of the method.

Numerical Approaches for Solving Mixed Volterra-Fredholm Fractional Integro-Differential Equations

“…However, the difficulty of finding the exact solution for many classes of these equations enforce researchers to solve them approximately using different numerical methods. For example, they use the Polynomial Least Squares Method [5], the Reproducing Kernel Method [6,7], Fractional Power Series Method [8], Haar wavelet [9], Laplace Adomian decomposition method [10], Homotopy perturbation method [11].…”