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This paper is concerned with a fractional diffusion predator-prey system with Holling type-II functional response in a bounded domain with no flux boundary condition. The local and global stabilities are investigated and sufficient conditions of stabilities are obtained. The existence of the non-constant steady states is considered and the sufficient conditions of the existence for the non-constant steady states are also obtained. The results show that the predator and the prey can coexist under some suitable conditions with fractional diffusion. [ABSTRACT FROM AUTHOR]

In this paper we consider a family of singularly perturbed delay differential equation of convection diffusion type. When the perturbation parameter is very small, the solution of the problem exhibits layer behavior. In the layer region the solution changes rapidly, while away from this region the change in the solution is moderate. This simultaneous presence of two different scales phenomena makes the problem stiff. In this work, the problem is solved by applying a new Liouville-Green transform and the asymptotic solutions are obtained. Application to multi-point boundary value problem is also illustrated. Several test examples are taken into account so as to test the efficiency of the proposed method. The method presented is compared with other existing numerical or asymptotic methods. It is observed that the method presented is very easy to implement and is capable of reducing the size of calculations significantly while still maintaining high accuracy of the solution. [ABSTRACT FROM AUTHOR]