Positive solution of singular boundary value problem for nonlinear fractional differential equation with nonlinearity that changes sign

Positivity ◽  
2011 ◽  
Vol 16 (1) ◽  
pp. 177-193 ◽  
Author(s):  
Shuqin Zhang
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

scholarly journals The Existence of Positive Solution to Three-Point Singular Boundary Value Problem of Fractional Differential Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Yuansheng Tian ◽  
Anping Chen
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Fixed Point Index Theory ◽  
Fractional Differential

We investigate the existence of positive solution to nonlinear fractional differential equation three-point singular boundary value problem:Dqu(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)=αD(q−1)/2u(t)|t=ξ, where1<q≤2is a real number,ξ∈(0,1/2],α∈(0,+∞)andαΓ(q)ξ(q−1)/2<Γ((q+1)/2),Dqis the standard Riemann-Liouville fractional derivative, andf∈C((0,1]×[0,+∞),[0,+∞)),lim⁡t→+0f(t,⋅)=+∞(i.e.,fis singular att=0). By using the fixed-point index theory, the existence result of positive solutions is obtained.

scholarly journals Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Jun-Rui Yue ◽  
Jian-Ping Sun ◽  
Shuqin Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solution ◽  
Fractional Differential Equation ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii Fixed Point Theorem ◽  
Fractional Differential

We consider the following boundary value problem of nonlinear fractional differential equation:(CD0+αu)(t)=f(t,u(t)),  t∈[0,1],  u(0)=0,   u′(0)+u′′(0)=0,  u′(1)+u′′(1)=0, whereα∈(2,3]is a real number, CD0+αdenotes the standard Caputo fractional derivative, andf:[0,1]×[0,+∞)→[0,+∞)is continuous. By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.

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