Abstract
In this article, the multi-step differential transform method (MsDTM) is applied to give approximate solutions of nonlinear ordinary differential equation such as fractional-non-linear oscillatory and vibration equations. The results indicate that the method is very effective and sufficient for solving nonlinear differential equations of fractional order.
Highlights
The Rayleigh equation determines a typical non-linear system with one degree of freedom which admitsA
The main aim of this paper is to extend the application of the multi-step differential transform method [30, 31] to solve a fractional order non-linear oscillator and vibration equation
We introduce the multi-step fractional differential transform method used in this paper to obtain approximate analytical solutions for the fractional differential equations (1)
Summary
The DTM gives exact values of the nth derivative of an analytic function at a point in terms of known and unknown boundary conditions in a fast manner. This method constructs, for differential equations, an analytical solution in the form of a polynomial. It is different from the traditional high order Taylor series method, which requires symbolic computations of the necessary derivatives of the data functions. The main aim of this paper is to extend the application of the multi-step differential transform method [30, 31] to solve a fractional order non-linear oscillator and vibration equation. The conclusions are given in the final Sect. 5
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