Solving nonlinear space-time fractional differential equations via ansatz method

Document Type : Research Paper


1 Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri, Turkey

2 Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir, Turkey


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 Kuznetsov Benjamin Bona Mahony (ZK-BBM) equation, the space-time fractional Klein-Gordon equation and the space-time fractional modified Regularized Long Wave (RLW) equation. This method can be suitable and more powerful for solving other kinds of nonlinear FDEs arising in mathematical physics.