Laplace Variational Iteration Method for Solving Conformable Fractional Order Integro-Differential Equations

This paper aims to integrate the Laplace transformation method with the variational iteration method to deliver an analytical approximate solution for fractional-order integro-differential equations, where the fractional-order derivative and integration are defined in the conformable sense. The iterative solution sequence is obtained using the Laplace variational iteration method, and the convergence of this sequence of approximate solutions to the exact solution is established and demonstrated. First, we shall study the approximate solution of a linear fractional integrodifferential equation, and secondly, solve the nonlinear fractional integro-differential equations modeled using conformable differointegration. Some illustrative examples are considered to verify the validity and accuracy of the proposed technique, in which approximate solutions are compared with the exact solutions if they exist. Through the comparison, we conclude that the present hybrid approach is very effective for solving this type of problem.