In this article, fractional complex transform with optimal homotopy analysis method (OHAM) is used to obtain numerical and analytical solutions for the nonlinear time-space fractional Fornberg-Whitham. Fractional complex transform is proposed to convert time-space fractional Fornberg-Whitham equation to the nonlinear ordinary differential equations and then applied OHAM to the new obtained equa...

We numerically investigate the dynamical behavior of the fractional-order Chua’s system. By utilizing the multistep generalized differential transform method MSGDTM , we find that the fractional-order Chua’s system with “effective dimension” less than three can exhibit chaos as well as other nonlinear behavior. Numerical results are presented graphically and reveal that the multistep generalize...

The multistep differential transform method is first employed to solve a time-fractional enzyme kinetics. This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations of fractional order. The fractional derivatives are described in the Caputo sense. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of...

In this paper, Sumudu decomposition method is developed to solve general form of fractional partial differential equation. The proposed method is based on the application of Sumudu transform to nonlinear fractional partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivatives are described in the Caputo sense. The Sumud...

In this paper an approximate analytical solution of the fractional Zakharov-Kuznetsov equations will be obtained with the help of the reduced differential transform method (RDTM). It is indicated that the solutions obtained by the RDTM are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

in this paper two different methods are presented to approximate the solution of the fractional black-scholes equation for valuation of barrier option. also, the two schemes need less computational work in comparison with the traditional methods. in this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

IIn this research work, we have shown that it is possible to use fuzzy transform method (FTM) for the estimate solution of fractional system differential equations (FSDEs). In numerical methods, in order to estimate a function on a particular interval, only a restricted number of points are employed. However, what makes the F-transform preferable to other methods is that it makes use of all poi...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

The objective of our work is to couple the Elzaki transform method and local fractional derivative which called transform, where we have provided important results this transformation as Laplace-Elzaki duality, integral convolution, also presented properties some special functions with sense. was applied solve linear differential equations in order obtain non-differentiable analytical solutions...