In the present paper, series solutions and approximate of time–space fractional differential equations are obtained using two different analytical methods. One is homotopy perturbation Sumudu transform method (HPSTM), another variational iteration Laplace (VILTM). It observed that very close to exact solutions. The useful significant analyze many phenomena, have not been reported in previous li...

Abstract Using a series of fractional powers we present representation the solution to logistic equation is presented. To simplify consider simplest case and prove that power indeed exact solution. Some numerical approximations are presented show good obtained by truncating series.

In this paper, we consider fractional reaction-diffusion equations with linear and nonlinear fractional reaction terms in a semi-infinite domain. Using q-Homotopy Analysis Method, solutions to these equations are obtained in the form of general recurrence relations. Closed form solutions in the form of the Mittag-Leffler function are perfectly obtained in the case with linear fractional reactio...

The exact solutions in the wave form are derived for the time fractional KdV and the time fractional Burgers’ equations in conformable fractional derivative sense. The fractional variable change using the fundamental properties of the conformable derivative reduces both equations to some nonlinear ODEs. The predicted solution is assumed to be a finite series form of a function satisfying a part...

A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered a...

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution....

Series solution of nonlinear dynamic system containing fractional derivative is obtained by the homotopy analysis method (HAM). The solution via HAM has auxiliary parameter h̄ which can control the convergent of the series to obey the exact or numerical solution. The model of viscoelastic behavior of a one-degree-of-freedom oscillator consisting of a discrete mass and a viscoelastic spring is co...