Solution of Conformable Fractional Ordinary Differential Equations via Differential Transform Method

Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions, Gronwall's inequality, integration by parts, Taylor power series expansions is developed in [2]. In this paper, we give conformable fractional differential transform method and its application to conformable fractional differential equations

Solutions around a regular a singular point of a sequential conformable fractional differential equation

In this work, firstly, some concepts of conformable fractional calculus in literature are given. Secondly, definitions of alpha-analytic point, a-ordinary point and regular a singular point are presented. Finally, the fractional power series solutions are given around a regular-singular point, in the case of variable coefficients for homogeneous sequential linear conformable fractional differential equations of order 2 alpha

Existence and uniqueness theorems for sequential linear conformable fractional differential equations

Recently, a new definition of fractional derivative called as the conformable fractional derivative which based on limits introduced by Khalil et al (2014). Later, Abdeljawad (2015) improved these definitions and gave the basic concepts in this new fractional calculus. In this paper, we generalize Abel's formula and Wronskian determinant definition and establish existence and uniqueness theorems for sequential linear conformable fractional differential equations

Numerical Simulation of Fractional Fornberg-Whitham Equation by Differential Transformation Method

An approximate analytical solution of fractional Fornberg-Whitham equation was obtained with the help of the two-dimensional differential transformation method (DTM). It is indicated that the solutions obtained by the two-dimensional DTM are reliable and present an effective method for strongly nonlinear partial equations. Exact solutions can also be obtained from the known forms of the series solutions

Solution of Nonlinear Oscillators with Fractional Nonlinearities by Using the Modified Differential Transformation Method

In this paper, an aproximate analytical method called the differential transform method (DTM) is used as a tool to give approximate solutions of nonlinear oscillators with fractional nonlinearites. The differential transformation method is described in a nuthsell. DTM can simply be applied to linear or nonlinear problems and reduces the required computational effort. The proposed scheme is based on the differential transform method (DTM), Laplace transform and Padé approximants. The results to get the differential transformation method (DTM) are applied Padé approximants. The reliability of this method is investigated by comparison with the classical fourth-order Runge–Kutta (RK4) method and Cos-AT and Sine-AT method. Our the presented method showed results to analytical solutions of nonlinear ordinary differential equation. Some plots are gived to shows solutions of nonlinear oscillators with fractional nonlinearites for illustrating the accurately and simplicity of the methods