Solution of Nonlinear Space–time Fractional Differential Equation via the Triple Fractional Riccati Expansion Method
E. A. B. Abdel-Salam *
Department of Mathematics, Faculty of Science, Assiut University, New Valley Branch, El-Kharja 72511, Egypt and Department of Mathematics, Faculty of Science, Northern Border University, Arar, Saudi Arabia.
M. S. Jazmati
Department of Mathematics, Faculty of Science, Qassim University, Baraudah, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
In this paper, the triple fractional Riccati expansion method is applied to solve fractional differential equation. To illustrate the effectiveness of the method, the nonlinear space-time fractional Klein–Gordon equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time.
Keywords: Triple fractional Riccati expansion method, nonlinear fractional differential equation, modified Riemann–Liouville derivative, exact solution, nonlinear space-time fractional Klein–Gordon equation.