In this paper, the projective Riccati equation method is applied to find exact solutions for fractional partial differential equations in the sense of modified RiemannLiouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the vali...

We propose a new approach for solving fractional partial differential equations based on a nonlinear fractional complex transformation and the general Riccati equation and apply it to solve the nonlinear time fractional biological population model and the (4+1)-dimensional space-time fractional Fokas equation. As a result, some new exact solutions for them are obtained.This approach can be suit...

some preliminaries about the integrable families of riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional schrodinger equation with the kerr law nonlinearity. finally by using of this method and solutions of ri...

In this paper, a new fractional Riccati equation rational expansion method is proposed to establish new exact solutions for fractional differential equations. For illustrating the validity of this method, we apply it to the nonlinear fractional Sharma-TassoOlever (STO) equation, the nonlinear time fractional biological population model and the nonlinear fractional foam drainage equation. Compar...

Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...

In this paper, we are concerned with seeking exact solutions for fractional differential-difference equations by an extended Riccati sub-ODE method. The fractional derivative is defined in the sense of the modified Riemann-liouville derivative. By a combination of this method and a fractional complex transformation, the iterative relations from indices n to n ± 1 are established. As for applica...

In this article, the backstepping control scheme is proposed to stabilize fractional order Riccati matrix differential equation with retarded arguments in which derivative presented using Caputo's definition of derivative. The results are established Mittag-Leffler stability. Lyapunov function defined at each stage and negativity an overall ensured by proper selection law. Numerical simulation ...

Abstract The fractional wave equation is presented as a generalization of the wave equation when arbitrary fractional order derivatives are involved. We have considered variable dielectric environments for the wave propagation phenomena. The Jumarie’s modified Riemann-Liouville derivative has been introduced and the solutions of the fractional Riccati differential equation have been applied to ...