scholarly journals On the periodic boundary value problem for Duffing type fractional differential equation with p-Laplacian operator

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Hua Jin ◽  
Wenbin Liu
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Periodic Boundary Value Problem ◽  
Laplacian Operator ◽  
Fractional Differential

PERIODIC BOUNDARY VALUE PROBLEM FOR FRACTIONAL DIFFERENTIAL EQUATION

2012 ◽  
Vol 23 (10) ◽  
pp. 1250100 ◽  
Author(s):  
ZHIGANG HU ◽  
WENBIN LIU ◽  
WENJUAN RUI
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Periodic Boundary Value Problem ◽  
Fractional Differential

In this paper, by using the coincidence degree theory, we consider periodic boundary value problem for fractional differential equation. A new result on the existence of solutions for above fractional boundary value problem is obtained.

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.

scholarly journals Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation withp-Laplacian Operator

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Jinhua Wang ◽  
Hongjun Xiang ◽  
ZhiGang Liu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Multiplicity ◽  
Fractional Differential

We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation withp-Laplacian operatorD0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0,0<t<1,u(0)=u′(1)=0,u′′(0)=0,D0+αu(t)|t=0=0, where0<γ<1,2<α<3,0<ρ⩽1,D0+αdenotes the Caputo derivative, andf:[0,1]×[0,+∞)×R→[0,+∞)is continuous function,ϕp(s)=|s|p-2s,p>1,  (ϕp)-1=ϕq,  1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works.

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