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Modelling is a portrait of complex natural or real world processes which enhances the knowledge of the mechanisms and provides assistance for prediction. In biology and bio medicine, organ malfunctioning of micro and macro level living populations can be understood through modelling and it helps to develop different methods to control. This paper considers the mathematical model of two species interaction using Caputo type fractional difference operator. The presence of chaos and its influence are studied in this work. The prey-predator fractional map's dynamic behaviour is validated experimentally by means of time series, bifurcation diagrams, chaotic and coexisting attractors. Further, adaptive control law is proposed to stabilize the fractional map and a control scheme is introduced to enhance the synchronization of the fractional model. Finally the effectiveness of the theoretical findings are demonstrated with numerical examples. [ABSTRACT FROM AUTHOR]

In this present work, we discuss the uniqueness of solutions of fractional order difference equations with boundary conditions of the form Δq1 u(l) + h(l + q1 − 1)g(u(l + q1 − 1)) = 0, for l ∈ [0,M]ℕ0 = {0,1,…,M}, u(q1− 2) = 0, Δu(q1 + M − 1) = 0 where g : [q1 − 1, q1 + M − 1]ℕq1 − 1 × ℝ → ℝ is continuous, h : [q1 − 1, q1 + M − 1]ℕq1 − 1 → [0, ∞) and 1 < q1 ≤ 2. We obtain some useful inequalities satisfied by the Green function for a given boundary value problem. Banach contraction principle is the main tool used here to establish the uniqueness of the solution. [ABSTRACT FROM AUTHOR]