Exact Solutions for Fractional Partial Differential Equations by Projective Riccati Equation Method
نویسنده
چکیده
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 validity of this method, we apply it to solve the space-time fractional Whitham-Broer-Kaup (WBK) equations and the time fractional Sharma-Tasso-Olever (STO) equation, and as a result, some new exact solutions for them are established.
منابع مشابه
Exact solutions for fractional partial differential equations by an extended fractional Riccati sub-equation method
In this paper, based on the fractional Riccati equation, we propose an extended fractional Riccati sub-equation method for solving fractional partial differential equations. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. By a proposed variable transformation, certain fractional partial differential equations are turned into fractional ordinary di...
متن کاملA new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics
In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...
متن کاملSolutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
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...
متن کاملExact solutions of a linear fractional partial differential equation via characteristics method
In recent years, many methods have been studied for solving differential equations of fractional order, such as Lie group method, invariant subspace method and numerical methods, cite{6,5,7,8}. Among this, the method of characteristics is an efficient and practical method for solving linear fractional differential equations (FDEs) of multi-order. In this paper we apply this method f...
متن کاملExact and numerical solutions of linear and non-linear systems of fractional partial differential equations
The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...
متن کامل