scholarly journals Computation of iterative solutions along with stability analysis to a coupled system of fractional order differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sajjad Ali ◽  
Thabet Abdeljawad ◽  
Kamal Shah ◽  
Fahd Jarad ◽  
Muhammad Arif
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Order ◽  
Coupled System ◽  
Fractional Order Differential Equations ◽  
Iterative Solutions

scholarly journals Bifurcation and Stability Analysis of a System of Fractional-Order Differential Equations for a Plant–Herbivore Model with Allee Effect

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 454 ◽  
Author(s):  
Ali Yousef ◽  
Fatma Bozkurt Yousef
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Fractional Order ◽  
Flip Bifurcation ◽  
Center Manifold Theorem ◽  
Fractional Order Differential Equations ◽  
Existence And Stability ◽  
Plant Herbivore Interaction ◽  
Plant Herbivore ◽  
Bifurcation And Stability

This article concerns establishing a system of fractional-order differential equations (FDEs) to model a plant–herbivore interaction. Firstly, we show that the model has non-negative solutions, and then we study the existence and stability analysis of the constructed model. To investigate the case according to a low population density of the plant population, we incorporate the Allee function into the model. Considering the center manifold theorem and bifurcation theory, we show that the model shows flip bifurcation. Finally, the simulation results agree with the theoretical studies.

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