Existence of positive solutions for nonlocal boundary value problem of fractional differential equation

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Xiping Liu ◽  
Legang Lin ◽  
Haiqin Fang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Nonlocal Boundary ◽  
Point Boundary ◽  
Nonlocal Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

AbstractIn this paper, we study a type of nonlinear fractional differential equations multi-point boundary value problem with fractional derivative in the boundary conditions. By using the upper and lower solutions method and fixed point theorems, some results for the existence of positive solutions for the boundary value problem are established. Some examples are also given to illustrate our results.

Existence of positive solutions for Riemann–Liouville fractional order three-point boundary value problem

2015 ◽  
Vol 08 (04) ◽  
pp. 1550057 ◽  
Author(s):  
Sabbavarapu Nageswara Rao
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions

In this paper, we study the following fractional order three-point boundary value problem [Formula: see text] where [Formula: see text], are the standard Riemann–Liouville fractional order derivatives with [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]: [Formula: see text] is continuous. By using several well-known fixed-point theorems in a cone, the existence of at least one and two positive solutions is obtained. Some examples are presented to illustrate the main results.

scholarly journals Positive Solutions to a Fractional-Order Two-Point Boundary Value Problem with p-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Xiangshan Kong ◽  
Haitao Li
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Operator Equation ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Laplacian Operator ◽  
Point Boundary ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions

This paper systematically investigates positive solutions to a kind of two-point boundary value problem (BVP) for nonlinear fractional differential equations with p-Laplacian operator and presents a number of new results. First, the considered BVP is converted to an operator equation by using the property of the Caputo derivative. Second, based on the operator equation and some fixed point theorems, several sufficient conditions are presented for the nonexistence, the uniqueness, and the multiplicity of positive solutions. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are effective.

scholarly journals Positive Solutions for Nonlinear First-Orderm-Point Boundary Value Problem on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
İsmail Yaslan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Time Scale ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Point Boundary ◽  
First Order ◽  
Existence Of Positive Solutions

By means of fixed-point theorems, we investigate the existence of positive solutions for nonlinear first-order -point boundary value problem , , where is a time scale, , are given constants.

scholarly journals An Analysis on the Positive Solutions for a Fractional Configuration of the Caputo Multiterm Semilinear Differential Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Sh. Rezapour ◽  
B. Azzaoui ◽  
B. Tellab ◽  
S. Etemad ◽  
H. P. Masiha
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Caputo Fractional Derivatives ◽  
Control Functions ◽  
Existence Of Positive Solutions ◽  
Semilinear Differential Equation ◽  
The Given ◽  
Existence Criteria

In this paper, we consider a multiterm semilinear fractional boundary value problem involving Caputo fractional derivatives and investigate the existence of positive solutions by terms of different given conditions. To do this, we first study the properties of Green’s function, and then by defining two lower and upper control functions and using the wellknown Schauder’s fixed-point theorem, we obtain the desired existence criteria. At the end of the paper, we provide a numerical example based on the given boundary value problem and obtain its upper and lower solutions, and finally, we compare these positive solutions with exact solution graphically.

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