A Modified Analytical Approach for Fractional Discrete KdV Equations Arising in Particle Vibrations

In this paper, we present an effectiveness of the proposed analytical algorithm for nonlinear time fractional discrete KdV equations. The discrete KdV equation play an important role in modeling of complicated physical phenomena such as particle vibrations in lattices, current flow in electrical flow and pulse in biological chains. The proposed algorithm is amagalation of the homotopy analysis method, Laplace transform method and homotopy polynomials. First, we present an alternative framework of the proposed method which can be used simply and effectively to handle nonlinear problems arising in science and engineering. Then, mainly, we address the convergence study of nonlinear fractional differential equations with Laplace transform. Camparisons are made between the results of the proposed method and exact solutions. Illustrative examples are given to demonstrate the simplicity and efficiency of the proposed method. The new results reveal that the proposed method is explicit, efficient and easy to use.