This paper is devoted to investigating the numerical solution for a class of fractional diffusion-wave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the...

In this article, optimal homotopy-analysis method is used to obtain approximate analytic solution of the time-fractional diffusion equation with a given initial condition. The fractional derivatives are considered in the Caputo sense. Unlike usual Homotopy analysis method, this method contains at the most three convergence control parameters which describe the faster convergence of the solution...

In this paper, The analytical solution of the nonlinear Fornberg-Whitham equation with fractional time derivative was derived by means of the homotopy analysis method. The fractional derivatives are described in the Caputo sense. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained. The results r...

In this paper, a class of fractional advection-dispersion models (FADMs) is considered. These models include five fractional advection-dispersion models, i.e., the times FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann-Liouville derivatives, the timespace FADM and the time fractional advection-diffusion-wave model with...

*Correspondence: [email protected] School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, PR China Abstract In this paper, we study boundary-value problems for the following nonlinear fractional differential equations involving the Caputo fractional derivative: D0+x(t) = f (t, x(t), Dβ0+x(t)), t ∈ [0, 1], x(0) + x′(0) = y(x), ∫ 1 0 x(t)dt =m, x′′(0) = x′′′(0) = · · · = x(n–...

Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann–Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their present state is determined by all past states with special forms of weights. To obtain discrete maps from fractional differential equations, we use the equival...

In this paper, by introducing the fractional derivative in the sense of Caputo, the Adomian decomposition method is directly extended to study the coupled Burgers equations with timeand space-fractional derivatives. As a result, the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components. The figures show the effectiveness and good acc...

In this article, we analysed the approximate solutions of time-fractional Kawahara equation and modified equation, which describe propagation signals in transmission lines formation nonlinear water waves long wavelength region. An efficient technique, namely natural transform decomposition method, is used present study. Fractional derivatives are considered Caputo, Caputo–Fabrizio, Atangana–Bal...