scholarly journals Existence and stability analysis to a coupled system of implicit type impulsive boundary value problems of fractional-order differential equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Arshad Ali ◽  
Kamal Shah ◽  
Fahd Jarad ◽  
Vidushi Gupta ◽  
Thabet Abdeljawad
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Boundary Value ◽  
Coupled System ◽  
Fractional Order Differential Equations ◽  
Impulsive Boundary Value Problems ◽  
Existence And Stability

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.

scholarly journals Mild solution of fractional order differential equations with not instantaneous impulses

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Pei-Luan Li ◽  
Chang-Jin Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Mild Solution ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Order Differential Equations

AbstractIn this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.

scholarly journals Results for Mild solution of fractional coupled hybrid boundary value problems

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Hossein Jafari ◽  
Hasib Khan ◽  
Sarah Jane Johnston
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Mild Solution ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Coupled System ◽  
Banach Contraction ◽  
Fractional Differential

AbstractThe study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray–Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.

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