Solving nonlinear partial differential equations of fractional order using an analytical method

In this article, we use an analytical method based on the solutions of the Riccati equation to solve nonlinear partial differential equations of fractional order. In this method, we first convert the fractional partial differential equations into an ordinary differential equation using Riemann-Liouville derivatives and a suitable transformation, then we consider the solutions of these equations as a finite series and using the solution of the equation Riccati's differential, we get the desired solutions. In this method, different types of solutions such as trigonometric, hyperbolic and exponential solutions are obtained. The results show that the method used in this article is very useful and effective for obtaining the solutions of fractional partial differential equations.

کلیدواژه ها:

Riemann-Liouville fractional derivative ، Mittag leffler -Leffler function ، Klein-Gordon equation ، biological population model equation