scholarly journals Boundary Value Problems of Nonlinear Mixed-Type Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ping Yu ◽  
Hongju Li ◽  
Jian Ding ◽  
Yanli Ma
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Point Theorem ◽  
Mixed Type ◽  
Boundary Value ◽  
Singular Differential Equation ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, by means of a fixed point theorem for monotone decreasing operators on a cone, we discuss the existence of positive solutions for boundary value problems of nonlinear fractional singular differential equation. The proof of the main result is based on Gatica–Oliker–Waltman fixed-point theorem. At last, an example is given to illustrate our main conclusion.

The Existence of Positive Solutions for Boundary Value Problems of Fractional Differential Equation

2014 ◽  
Vol 711 ◽  
pp. 303-307 ◽  
Author(s):  
Jie Gao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, by using Leggett-Williams fixed point theorem, we will study the existence of positive solutions for a class of multi-point boundary value problems of fractional differential equation on infinite interval.

scholarly journals Positive solutions of boundary value problems for p-Laplacian fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1265-1277 ◽  
Author(s):  
Fatma Fen ◽  
Ilkay Karac ◽  
Ozlem Ozen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.

scholarly journals Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yunhong Li ◽  
Weihua Jiang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Fractional Differential

In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. We also give some examples to illustrate the effectiveness of our main results.

Existence of positive solutions for systems of nonlinear fractional differential equation with p-Laplacian

2019 ◽  
Vol 13 (05) ◽  
pp. 2050089 ◽  
Author(s):  
S. Nageswara Rao ◽  
Meshari Alesemi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we establish sufficient conditions for the existence of positive solutions for a system of nonlinear fractional [Formula: see text]-Laplacian boundary value problems under different combinations of superlinearity and sublinearity of the nonlinearities via the Guo–Krasnosel’skii fixed point theorem. Moreover, an example is given to illustrate our results.

scholarly journals EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS

2003 ◽  
Vol 46 (2) ◽  
pp. 279-292 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem

AbstractIn this paper we consider the existence of positive solutions to the boundary-value problems\begin{align*} (p(t)u')'-q(t)u+\lambda f(t,u)\amp=0,\quad r\ltt\ltR, \\[2pt] au(r)-bp(r)u'(r)\amp=\sum^{m-2}_{i=1}\alpha_iu(\xi_i), \\ cu(R)+dp(R)u'(R)\amp=\sum^{m-2}_{i=1}\beta_iu(\xi_i), \end{align*}where $\lambda$ is a positive parameter, $a,b,c,d\in[0,\infty)$, $\xi_i\in(r,R)$, $\alpha_i,\beta_i\in[0,\infty)$ (for $i\in\{1,\dots m-2\}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15

Positive solutions of superlinear boundary value problems

1981 ◽  
Vol 88 (1-2) ◽  
pp. 17-24 ◽  
Author(s):  
Heinrich Voss
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Image Position

SynopsisUsing a fixed point theorem on operators expanding a cone in a Banach space we prove the existence of positive solutions of superlinear boundary value problemsAt the same time we get bounds (or even inclusions) of positive solutions.

scholarly journals Existence criteria of positive solutions for fractional p-Laplacian boundary value problems

Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3789-3799
Author(s):  
Deren Yoruk ◽  
Tugba Cerdik ◽  
Ravi Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Existence Criteria

By means of the Bai-Ge?s fixed point theorem, this paper shows the existence of positive solutions for nonlinear fractional p-Laplacian differential equations. Here, the fractional derivative is the standard Riemann-Liouville one. Finally, an example is given to illustrate the importance of results obtained.

scholarly journals Boundary value problems for impulsive fractional differential equations in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5603-5616 ◽  
Author(s):  
Shuai Yang ◽  
Shuqin Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Point Theorem ◽  
Boundary Value ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

This paper is devoted to studying the existence and uniqueness of solutions to the boundary value problems for a impulsive fractional differential equation in Banach spaces. The arguments are based upon the methods of noncompact measure, Banach fixed point theorem and Krasnoselskii?s fixed point theorem. Some examples are given to demonstrate the application of our main results.

scholarly journals Existence of positive solutions for second-order impulsive time scale boundary value problems on infinite intervals

Filomat ◽  
2014 ◽  
Vol 28 (10) ◽  
pp. 2163-2173
Author(s):  
Ismail Yaslan ◽  
Zehra Haznedar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Time Scale ◽  
Boundary Value ◽  
Second Order ◽  
Existence Of Positive Solutions ◽  
Infinite Intervals

In this paper, we consider nonlinear second order m-point impulsive time scale boundary value problems on infinite intervals. By using Leray-Schauder fixed point theorem, Avery-Henderson fixed point theorem and the five functional fixed point theorem, respectively, we establish the criteria for the existence of at least one, two and three positive solutions to the nonlinear impulsive time scale boundary value problems on infinite intervals.

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

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