Multiple Positive Solutions to $$m$$ m -Point Boundary Value Problem of Nonlinear Fractional Differential Equation

2013 ◽  
Vol 23 (1) ◽  
pp. 43-56
Author(s):  
Yuansheng Tian
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

scholarly journals Positive Solutions for Three-Point Boundary Value Problem of Fractional Differential Equation with -Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shang-lin Yao ◽  
Guo-hui Wang ◽  
Zhi-ping Li ◽  
Li-jun Yu
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Fractional Differential

We investigate the existence of multiple positive solutions for three-point boundary value problem of fractional differential equation with -Laplacian operator , where are the standard Riemann-Liouville derivatives with , and the constant is a positive number satisfying ; -Laplacian operator is defined as . By applying monotone iterative technique, some sufficient conditions for the existence of multiple positive solutions are established; moreover iterative schemes for approximating these solutions are also obtained, which start off a known simple linear function. In the end, an example is worked out to illustrate our main results.

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