in this paper, we consider the inhomogeneous time-fractional nonlinear fisher equation with three known boundary conditions. we first apply a modified homotopy perturbation method for translating the proposed problem to a set of linear problems. then we use the separation variables  method to solve obtained problems. in examples, we illustrate that by right choice of source term in the modified...

The Fisher equation with inhomogeneous forcing is considered in this paper. First, a forced Fisher equation and boundary conditions are derived. Then, the existence of a local solution for the forced equation with a homegeneous Dirichlet condition is proved by Galerkin’s method. Next, a maximum principle is established and the existence of a global solution is obtained as a consequence of the m...

Kudryashov in [ Phys. Lett. A 342 (2005) 99-106] used simplest nonlinear differential equations like the Riccati equation, the equation for the Jacobi elliptic function to present a new approach for searching exact solutions of nonlinear partial differential equations. As application, he obtained a kind of exact solutions to the Fisher equation. In this letter, more explicit exact solitary wave...

We perform the analysis of a hyperbolic model which is the analog of the Fisher-KPP equation. This model accounts for particles that move at maximal speed ε (ε > 0), and proliferate according to a reaction term of monostable type. We study the existence and stability of traveling fronts. We exhibit a transition depending on the parameter ε: for small ε the behaviour is essentially the same as f...