In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...

in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous sub-diffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and conv...