Stability Analysis and Computational Interpretation of an Effective Semi Analytical Scheme for Fractional Order Non-Linear Partial Differential Equations

Abstract

In this study we will check the stability of the semi analytical technique, the Laplace variational iteration (LVI) scheme, which is the combination of a variational iteration technique and the Laplace transform method. Then, we will apply it to solve some non-linear fractional order partial differential equations. Since the Laplace transform cannot be applied to non-linear problems, the combination of the variational iteration technique with it will give a better and rapidly convergent sequence. Exact solutions may also exist, but we will show that the coupled technique is much better to approximate the exact solutions. The Caputo–Fabrizio fractional derivative will be used throughout the study. In addition, some possible implications of the results given here are connected with fixed point theory.