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.

Multiple positive solutions of nonlinear fractional differential equations with integral boundary value conditions

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Wei Sun ◽  
Youyu Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Fractional Differential

AbstractIn this paper, we consider the multiplicity of positive solutions for a class of nonlinear boundary-value problem of fractional differential equations with integral boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to the integral boundary value problem.

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 Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

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