In this study, a fractional Bernstein series solution method has been submitted to solve the fractional-order biological population model with one carrying capacity. The numerical implemented by an effective algorithm written on computer algebraic system Maple 15. An error-bound analysis is performed using process similar RK45 method. error estimation technique relating residual function presen...

Seasonal changes in the diel feeding patterns of the zooplanktivorous icefish (Neosalanx taihuensis), which is an endemic species of China, were studied in the large, shallow eutrophic Lake Chaohu of China during the autumn of 2002 and summer of 2003. The results of the diel feeding rhythm indicate that icefish is a visual particulate feeder. There were large differences in diet composition and...

In this manuscript, we investigate the dynamics behavior of a fractional-order Leslie-Gower model by considering fear effect in prey and Allee predators. Firstly, all possible equilibrium points are analyzed identifying conditions their existence local stability. Here, find four points, where two stable unstable points. Furthermore, also stability changing caused Hopf bifurcation when order der...

We consider a Leslie-Gower model with the Beddington-DeAngelis functional response, Allee effect, and Caputo fractional order derivative. first establish existence, uniqueness, non-negativity, boundedness of solutions to confirm biological feasibility model. Moreover, Lyapunov direct method including generalized LaSalle invariance principle is applied investigate global stability prey-free poin...

We have investigated wave solutions of the Predator–Prey (PP) model with fractional derivative order by novel three modified mathematical methods help Mathematica platform. The derived are in form distinct functions such as trigonometric, hyperbolic, exponential and rational functional. For physical phenomena model, some plotted 2-dimensional 3-dimensional inserting specific values to attached ...

in this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the lipschitz type condition. moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.