Homotopy analysis method for higher-order fractional integro-differential equations

Homotopy analysis method for systems of fractional integro-differential equations

In this article, based on the homotopy analysis method (HAM), a new analytic technique is proposed to solve systems of fractional integro-differential equations. Comparing with the exact solution, the HAM provides us with a simple way to adjust and control the convergence region of the series solution by introducing an auxiliary parameter h . Four examples are tested using the proposed techniqu...

Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations

A NEW MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING LINEAR SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.  

He’s Homotopy Perturbation Method for Nonlinear Ferdholm Integro-Differential Equations Of Fractional Order

In this paper, homotopy perturbation method is applied to solve non-linear Fredholm integrodifferential equations of fractional order. Examples are presented to illustrate the ability of the method. The results reveal that the proposed methods very effective and simple and show that this method can be applied to the non-fractional cases.

A spectral method based on Hahn polynomials for solving weakly singular fractional order integro-differential equations

In this paper, we consider the discrete Hahn polynomials and investigate their application for numerical solutions of the fractional order integro-differential equations with weakly singular kernel .This paper presented the operational matrix of the fractional integration of Hahn polynomials for the first time. The main advantage of approximating a continuous function by Hahn polynomials is tha...