Existence and Asymptotic Behavior of Positive Solutions for a Coupled System of Semilinear Fractional Differential Equations

2016 ◽  
Vol 71 (3-4) ◽  
pp. 705-730 ◽  
Author(s):  
Hassan Yahya Alfifi ◽  
Imen Ben Saad ◽  
Sameh Turki ◽  
Zagharide Zine El Abidine
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Fractional Differential

scholarly journals On the Asymptotic Behavior of Positive Solutions of Certain Fractional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Said R. Grace
Keyword(s):  
Asymptotic Behavior ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Real Constant ◽  
Fractional Differential

This paper deals with the asymptotic behavior of positive solutions of certain forced fractional differential equations of the formDcαCyt=et+ft, xt,c>1,α∈0,1, whereyt=atx′t′,c0=y(c)/Γ(1) =yc, andc0is a real constant. From the obtained results, we derive a technique which can be applied to some related fractional differential equations.

scholarly journals Positive Solutions for Coupled Nonlinear Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Wenning Liu ◽  
Xingjie Yan ◽  
Wei Qi
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Cartesian Product ◽  
Coupled System ◽  
Integral Boundary ◽  
Nonlinear Fractional Differential Equations ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two conesK1,K2and computing the fixed point index in product coneK1×K2, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.

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