A boundary value problem for fractional differential equation with -Laplacian operator at resonance

2012 ◽  
Vol 75 (6) ◽  
pp. 3210-3217 ◽  
Author(s):  
Taiyong Chen ◽  
Wenbin Liu ◽  
Zhigang Hu
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Laplacian Operator ◽  
At Resonance ◽  
Fractional Differential

scholarly journals Studies on BVPs for IFDEs involved with the Riemann-Liouville type fractional derivatives

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Boundary Value ◽  
Resonance Case ◽  
Liouville Type ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
At Resonance ◽  
Fractional Differential

AbstractIn this article, we present a new method for converting the boundary value problems for impulsive fractional differential systems involved with the Riemann-Liouville type derivatives to integral systems, some existence results for solutions of a class of boundary value problems for nonlinear impulsive fractional differential systems at resonance case and non-resonance case are established respectively. Our analysis relies on the well known Schauder’s fixed point theorem and coincidence degree theory. Examples are given to illustrate main results. This paper is motivated by [Solvability of multi-point boundary value problem of nonlinear impulsive fractional differential equation at resonance, Electron. J. Qual. Theory Differ. Equ. 89(2011), 1-19], [Existence result for boundary value problem of nonlinear impulsive fractional differential equation at resonance, J, Appl, Math, Comput. 39(2012) 421-443] and [Solvability for a coupled system of fractional differential equations with impulses at resonance, Bound. Value Probl. 2013, 2013: 80].

scholarly journals Existence of Solutions of Fractional Differential Equation withp-Laplacian Operator at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhigang Hu ◽  
Wenbin Liu ◽  
Jiaying Liu
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Fractional Boundary Value Problem ◽  
Mawhin’S Continuation Theorem ◽  
Laplacian Equation ◽  
At Resonance ◽  
Fractional Differential

By using the extension of Mawhin’s continuation theorem due to Ge, we consider boundary value problems for fractionalp-Laplacian equation. A new result on the existence of solutions for the fractional boundary value problem is obtained, which generalizes and enriches some known results to some extent from the literature.

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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