Lie group method and fractional differential equations

Zedan, Hassan A.; Abu-Nawas, M.

doi:10.22436/jnsa.010.08.13

Cited by 3 publications

(1 citation statement)

References 17 publications

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“…In the case of some nonlinear ordinary differential system, Shang [14][15][16] introduced the Lie algebra approach to obtain exact solutions. The exact solutions of some nonlinear fractional differential equations may also be found using similar method (see, for example, [17,18]). In the Lie algebra method, the solution is constructed from the symmetry property of the model.…”

Section: Introductionmentioning

confidence: 99%

A Fractional-Order Predator–Prey Model with Ratio-Dependent Functional Response and Linear Harvesting

et al. 2019

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We consider a model of predator–prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity and boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon’s theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurrence of Hopf bifurcation around the interior point is also shown analytically. At the end, we implemented the Predictor–Corrector scheme to perform some numerical simulations.

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