May be this will help you - Trophic Cascades: Predators, Prey, and the Changing Dynamics of Nature, by John Terborgh and James A Estes, 2010; - Ecology of Predator-Prey Interactions, by Pedro Barbosa and Ignacio Castellanos, 2005; - Predator-Prey Dynamics: The Role of Olfaction, by Michael R Conover, 2007. 

Thanks Lavinia Lancu

Dear Shashi Kant,

If your model is "discrete", for example an insects population without generations overlapping (see J.R. Beddington, C.A. Free, J.H. Lawton. Nature, vol. 255, 1975, 58-60), in general it will be of Dim2 noninvertible map (recurrence relationship) type.

The problem of fractional iterates is mentioned (but not really dealt) in pp. 17, 70,71, 96, 100, 101 of the book: I. Gumowski & C. Mira "Recurrences and Discrete Dynamic Systems" lecture Notes in Mathematics n°809, Springer Verlag, 1980.

In the case of a Dim1 noninvertible recurrence, revealing the problem difficulties, the paper "Sur l'itération fractionnaire d'un endomorphisme quadratique", C. Mira, S. Mullenbach, C. R. Acad. Sciences Paris, série 1, t. 297, 369-372, 1983, shows how solve this topic.

Full text in my RG page, and the attached file.

https://www.researchgate.net/publication/263963761_Sur_l%27itration_fractionnaire_d%27un_endomorphisme_quadratique

The case of a Dim2 noninvertible recurrence, the problem is only approached in Chapter 8 (pp. 125-133) of the S. Mullenbach thesis "Contribution à l'étude de l'itération fractionnaire des endomorphismes" (Doctorat 3ème cycle, spécialité mathématiques appliquées, Université Paul Sabatier Toulouse, 26 mai 1983).

Best wishes of success for your research work.

C. Mira

Article Sur l'itération fractionnaire d'un endomorphisme quadratique

Sir C. Mira,

Very Nice Suggestion, but i am interested to study the Prey predator system with FDE (Fractional Differential Equation) with continuous derivatives.  

Shashi Kant

Have you seen Das and Gupta, Journal of Theoretical Biology 277 (2011) and references therein?

No Richard Williams sir, i will see it. Thanks