scholarly journals Iterative unique positive solutions for a new class of nonlinear singular higher order fractional differential equations with mixed-type boundary value conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Fang Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Mixed Type ◽  
Boundary Value ◽  
Higher Order ◽  
New Class ◽  
Fractional Differential ◽  
Type Boundary

scholarly journals Monotone and Concave Positive Solutions to Three-Point Boundary Value Problems of Higher-Order Fractional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wenyong Zhong ◽  
Lanfang Wang
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Fractional Differential

We study the three-point boundary value problem of higher-order fractional differential equations of the formDc0+ρut+ft, ut=0,0<t<1,2⩽n-1<ρ<n,u′(0)=u′′(0)=⋯=un-1(0)=0,u(1)+pu′(1)=qu′(ξ), where cD0+ρis the Caputo fractional derivative of orderρ, and the functionf:[0,1]×[0,∞)↦[0,+∞)is continuously differentiable. Here,0⩽q⩽p,0<ξ<1,2⩽n-1<ρ<n. By virtue of some fixed point theorems, some sufficient criteria for the existence and multiplicity results of positive solutions are established and the obtained results also guarantee that the positive solutions discussed are monotone and concave.

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.

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