Progress in Fractional Differentiation & Applications

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In this paper, a fractional dynamical model of Salmonella with time delay is studied numerically. The proposed model is administered by a system of fractional delay differential equations, where the fractional derivative is defined in the sense of the Caputo definition. The parameters are modified regarding to the order of the fractional derivative. The stability of the disease free equilibrium point and endemic equilibrium point is investigated for any time delay. Weighted difference numerical technique is introduced to simulate the proposed model. This scheme was unconditionally stable when the weight factor is less than 1. Numerical simulations with some comparison are introduced to show the applicability and effectivity of the proposed method to solve such stiff systems of fractional delay differential equations and to confirm the theoretical studies.

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