A hybrid technique for approximating the solution of fractional order integro differential equations

In this article, we present an effective approach for solving nonlinear fractional order integro-differential equations. The fractional order derivative will be in the Caputo sense. For this, we propose an approach combined the least squares method together with the Laplace transform and the shifted Legendre polynomials. Using the proposed approach we will converts the nonlinear fractional order integro-differential equation into a se of (N+1) algebraic equations, where the solution to the resultant equation provides us with the unknown coefficients of the infinite series that have been used to approximate the solution to the considered fractional order integro-differential equations. From the results of the given examples, one can conclude that the recommended approach in this article is simple to implement and accurate