Existence of Positive Solutions for Boundary Value Problem of Fractional Differential Equations with p-Laplacian Operator

2020 ◽  
Vol 09 (12) ◽  
pp. 2301-2307
Author(s):  
佳艳 段
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

scholarly journals The Existence of Positive Solutions for Fractional Differential Equations with Integral and Disturbance Parameter in Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Mei Jia ◽  
Xiping Liu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Disturbance Parameter ◽  
Fractional Differential

We study the existence and nonexistence of the positive solutions for the integral boundary value problem of the fractional differential equations with the disturbance parameterain the boundary conditions and the impact of the disturbance parameteraon the existence of positive solutions. By using the upper and lower solutions method, fixed point index theory and the Schauder fixed point theorem, we obtain sufficient conditions for that the problem has at least one positive solution, two positive solutions and no solutions. Under certain conditions, we also obtain the demarcation point which divides the disturbance parameters into two subintervals such that the boundary value problem has positive solutions for the disturbance parameter in one subinterval while no positive solutions in the other.

scholarly journals The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yanli Chen ◽  
Yongxiang Li
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Index Theory ◽  
Nonlinear Fractional Differential Equations ◽  
Fixed Point Index Theory ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem-D0+αu(t)=f(t,u(t)),   0<t<1,  u(0)=u'(0)=u'(1)=0,where2<α≤3is a real number,D0+αis the Riemann-Liouville fractional derivative of orderα, andfis a given continuous function. Our analysis relies on the fixed point index theory in cones.

scholarly journals Existence of positive solutions for a fractional compartment system

2021 ◽  
pp. 1-9
Author(s):  
Lingju Kong ◽  
Min Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Compartment System ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this article, we investigate the existence of positive solutions of a boundary value problem for a system of fractional differential equations. The resilience of a fractional compartment system is also studied to demonstrate the application of the result.

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

2014 ◽  
Vol 2014 ◽  
pp. 1-18 ◽  
Author(s):  
Min Jiang ◽  
Shouming Zhong
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Multiple Positive Solutions ◽  
Fractional Differential ◽  
Fixed Point Techniques

This paper investigates the existence, multiplicity, nonexistence, and uniqueness of positive solutions to a kind of two-point boundary value problem for nonlinear fractional differential equations withp-Laplacian operator. By using fixed point techniques combining with partially ordered structure of Banach space, we establish some criteria for existence and uniqueness of positive solution of fractional differential equations withp-Laplacian operator in terms of different value of parameter. In particular, the dependence of positive solution on the parameter was obtained. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are applicable.

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