Study On Approximate Solutions Of Two Fractional Differential Equations

Fractional differential equations have excited,in recent years,a considerable interest both in mathematics and in applications.Many important phenomena in electromagnetics,acoustics,viscoelasticity,electrochemistry,cosmology and material science are well described by fractional differential equations.The solution of a fractional differential equation is much involved.In general,there exists no method that yields an exact solution for a fractional differential equation.Therefore,the study of the study of approximate solutions of fractional differential equations has become a hot topic.Many methods have been proposed,such as Adomian decomposition method,variational iteration method and differential transform method.Elzaki transform,homotopy analysis method and homotopy perturbation method are also very important.In this paper,according to the combination of homotopy analysis method and Elzaki transform(ETHPM),we get the approximate solution of fractional biological population model,when the fractional derivative of ?(28)1 we could get the exact solution.The approximate solution of space fractional telegraph equation is also obtained by Elzaki transform combined with the homotopy perturbation method(ETHPM),the exact solution of the equation under specific conditions is also given.Three examples are given to verify the feasibility of the method,and the three-dimensional graphs of the solutions are drawn with the help of Mathematica.The advantage of the method used in this paper is that it can combine the two methods to solve the non-linear differential equation,making the solving process simple and systematic.The results show that Elzaki transform combined with homotopy analysis method and homotopy perturbation method are effective methods for solving approximate solutions of fractional differential equations.