A coupling method of Homotopy technique and Laplace transform for nonlinear fractional differential equations

Yang-Laplace transform method Volterra and Abel's integro-differential equations of fractional order

This study outlines the local fractional integro-differential equations carried out by the local fractional calculus. The analytical solutions within local fractional Volterra and Abel’s integral equations via the Yang-Laplace transform are discussed. Some illustrative examples will be discussed. The obtained results show the simplicity and efficiency of the present technique with application t...

Homotopy Perturbation Method and Aboodh Transform for Solving Nonlinear Partial Differential Equations

Here, a new method called Aboodh transform homotopy perturbation method(ATHPM) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and Aboodh transformto investigate some nonlinear partial dierential equations. The nonlinearterms can be handled by the use of homotopy perturbation method. The resultsshow the eciency of this me...

Approximate Solutions of Fractional Linear and Nonlinear Differential Equations Using Laplace Homotopy Analysis Method

In this paper, a Laplace homotopy analysis method which is based on homotopy analysis method and Laplace transform is applied to obtain the approximate solutions of fractional linear and non-linear differential equations. The proposed algorithm presents a procedure of constructing the set of base functions and gives a high-order deformation equation in simple form. Numerical examples are includ...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

Laplace Transform of Fractional Order Differential Equations

In this article, we show that Laplace transform can be applied to fractional system. To this end, solutions of linear fractional-order equations are first derived by a direct method, without using Laplace transform. Then the solutions of fractional-order differential equations are estimated by employing Gronwall and Hölder inequalities. They are showed be to of exponential order, which are nece...