Homotopy perturbation Laplace transform solution of fractional non-linear reaction diffusion system of Lotka-Volterra type differential equation

Homotopy Perturbation Method for the Coupled Fractional Lotka-volterra Equations

Fractional differential equations started to have important applications in various fields of science and engineering involving dynamics of complex phenomena. Finding new methods to solve the fractional differential equations is an open issue in the area of fractional calculus. In this paper the homotopy perturbation method is used to find an analytic approximate solution for the coupled Lotka-...

Numerical solutions of two-dimensional linear and nonlinear Volterra integral equations: Homotopy perturbation method and differential transform method

Homotopy perturbation method for solving fractional Bratu-type equation

In this paper, the homotopy perturbation method (HPM) is applied to obtain an approximate solution of the fractional Bratu-type equations. The convergence of the method is also studied. The fractional derivatives are described in the modied Riemann-Liouville sense. The results show that the proposed method is very ecient and convenient and can readily be applied to a large class of fractional p...

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...

Nonlinearities distribution Laplace transform-homotopy perturbation method

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we ...