scholarly journals The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yanli Chen ◽  
Yongxiang Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Index Theory ◽  
Nonlinear Fractional Differential Equations ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem-D0+αu(t)=f(t,u(t)),   0<t<1,  u(0)=u'(0)=u'(1)=0,where2<α≤3is a real number,D0+αis the Riemann-Liouville fractional derivative of orderα, andfis a given continuous function. Our analysis relies on the fixed point index theory in cones.

scholarly journals Positive Solutions to Boundary Value Problems of Nonlinear Fractional Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Yige Zhao ◽  
Shurong Sun ◽  
Zhenlai Han ◽  
Qiuping Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Nonlinear Fractional Differential Equation ◽  
Nonlinear Fractional Differential Equations ◽  
Nonexistence And Existence ◽  
Fractional Differential

We study the existence of positive solutions for the boundary value problem of nonlinear fractional differential equationsD0+αu(t)+λf(u(t))=0,0<t<1,u(0)=u(1)=u'(0)=0, where2<α≤3is a real number,D0+αis the Riemann-Liouville fractional derivative,λis a positive parameter, andf:(0,+∞)→(0,+∞)is continuous. By the properties of the Green function and Guo-Krasnosel'skii fixed point theorem on cones, the eigenvalue intervals of the nonlinear fractional differential equation boundary value problem are considered, some sufficient conditions for the nonexistence and existence of at least one or two positive solutions for the boundary value problem are established. As an application, some examples are presented to illustrate the main results.

scholarly journals The Existence of Positive Solutions for Fractional Differential Equations with Integral and Disturbance Parameter in Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Mei Jia ◽  
Xiping Liu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Disturbance Parameter ◽  
Fractional Differential

We study the existence and nonexistence of the positive solutions for the integral boundary value problem of the fractional differential equations with the disturbance parameterain the boundary conditions and the impact of the disturbance parameteraon the existence of positive solutions. By using the upper and lower solutions method, fixed point index theory and the Schauder fixed point theorem, we obtain sufficient conditions for that the problem has at least one positive solution, two positive solutions and no solutions. Under certain conditions, we also obtain the demarcation point which divides the disturbance parameters into two subintervals such that the boundary value problem has positive solutions for the disturbance parameter in one subinterval while no positive solutions in the other.

scholarly journals Existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with mixed-type boundary value conditions

2018 ◽  
Vol 24 (1) ◽  
pp. 73-94 ◽  
Author(s):  
Fang Wang ◽  
Lishan Liu ◽  
Debin Kong ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Mixed Type ◽  
Index Theory ◽  
Nonlinear Fractional Differential Equations ◽  
Fixed Point Index Theory ◽  
Fractional Differential ◽  
Type Boundary

In this article, we study a class of nonlinear fractional differential equations with mixed-type boundary conditions. The fractional derivatives are involved in the nonlinear term and the boundary conditions. By using the properties of the Green function, the fixed point index theory and the Banach contraction mapping principle based on some available operators, we obtain the existence of positive solutions and a unique positive solution of the problem. Finally, two examples are given to demonstrate the validity of our main results.

scholarly journals Existence of positive solutions for a fractional compartment system

2021 ◽  
pp. 1-9
Author(s):  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Compartment System ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this article, we investigate the existence of positive solutions of a boundary value problem for a system of fractional differential equations. The resilience of a fractional compartment system is also studied to demonstrate the application of the result.

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