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...

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...

In this paper we study the large-time behavior of solutions of one-dimensional fractional Fisher-KPP reaction-diffusion equations, when the initial condition is asymptotically frontlike and it decays at infinity more slowly than a power x−b, where b < 2α and α ∈ (0, 1) is the order of the fractional Laplacian. We prove that the level sets of the solutions move exponentially fast as time goes to...

We develop a heuristic model embedding Kleiber and Murray laws to describe mass growth, metastasis and vascularization in cancer. We analyze the relevant dynamics using different evolution equations (Verhulst, Gompertz and others). Their extension to reaction diffusion equation of the Fisher type is then used to describe the relevant metastatic spreading in space. Regarding this last point, we ...

The local fractional variational iteration method is applied to a modified Fisher?s equation defined on Cantor sets with the fractal conditions. solution process simple, and accuracy of approximate high. provides an unrivaled tool for differential equations. Key word: equation, analytical solutions, method, derivative

In a recent study, we investigate the Burgers–Fisher equation through developed scheme, namely, non-polynomial spline fractional continuity method. The proposed models represent nonlinear optics, chemical physics, gas dynamics, and heat conduction. basic concept of new approach is constructing with instead natural derivative. Furthermore, truncation error analyzed to determine order convergence...

It is argued that univariate long memory estimates based on ex post data tend to underestimate the persistence of ex ante variables (and, hence, that of the ex post variables themselves) because of the presence of unanticipated shocks whose short run volatility masks the degree of long range dependence in the data. Empirical estimates of long range dependence in the Fisher equation are shown to...

Numerous applied mathematics and physical applications, such as the simulation of financial mathematics, gas dynamics, nonlinear phenomena in plasma physics, fluid mechanics, ocean engineering, utilize time-fractional generalized Burgers–Fisher equation (TF-GBFE). This describes concept dissipation illustrates how reaction systems can be coordinated with advection. To examine analyze present ev...