Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Kaihong Zhao ◽  
Ping Gong
Keyword(s):  
Positive Solutions ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary ◽  
Nonlinear Coupled System ◽  
Krasnoselskii Fixed Point Theorem ◽  
Integral Boundary Value Problems ◽  
Eigenvalue Intervals

AbstractIn the paper, we investigate a class of four-point integral boundary value problems for the nonlinear coupled system involving higher-order Caputo fractional derivatives and Riemann-Stieltjes integral boundary conditions. By employing Guo-Krasnoselskii fixed point theorem, some sufficient conditions are obtained to guarantee the existence of at least one or two positive solutions for this system. Meanwhile, the eigenvalue intervals of existence for positive solutions are also given. As applications, some examples are provided to illustrate the validity of our main results.

scholarly journals POSITIVE SOLUTIONS OF NTH-ORDER BOUNDARY VALUE PROBLEMS WITH INTEGRAL BOUNDARY CONDITIONS

2015 ◽  
Vol 20 (2) ◽  
pp. 188-204 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak Fen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Integral Boundary

In this paper, by using double fixed point theorem and a new fixed point theorem, some sufficient conditions for the existence of at least two and at least three positive solutions of an nth-order boundary value problem with integral boundary conditions are established, respectively. We also give two examples to illustrate our main results.

Multiple positive solutions of nonlinear fractional differential equations with integral boundary value conditions

2014 ◽  
Vol 17 (3) ◽  
Author(s):  
Wei Sun ◽  
Youyu Wang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Fractional Differential

AbstractIn this paper, we consider the multiplicity of positive solutions for a class of nonlinear boundary-value problem of fractional differential equations with integral boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to the integral boundary value problem.

scholarly journals Study on Implicit-Type Fractional Coupled System with Integral Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 300
Author(s):  
Longfei Lin ◽  
Yansheng Liu ◽  
Daliang Zhao
Keyword(s):  
Boundary Conditions ◽  
Topological Degree ◽  
Fractional Derivatives ◽  
Existence Result ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Coupled System ◽  
Topological Degree Theory ◽  
Caputo Fractional Derivatives ◽  
Integral Boundary

This paper is concerned with a class of implicit-type coupled system with integral boundary conditions involving Caputo fractional derivatives. First, the existence result of solutions for the considered system is obtained by means of topological degree theory. Next, Ulam–Hyers stability and generalized Ulam–Hyers stability are studied under some suitable assumptions. Finally, one example is worked out to illustrate the main results.

scholarly journals Existence and Uniqueness of Solutions for the System of Nonlinear Fractional Differential Equations with Nonlocal and Integral Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Allaberen Ashyralyev ◽  
Yagub A. Sharifov
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

In the present study, the nonlocal and integral boundary value problems for the system of nonlinear fractional differential equations involving the Caputo fractional derivative are investigated. Theorems on existence and uniqueness of a solution are established under some sufficient conditions on nonlinear terms. A simple example of application of the main result of this paper is presented.

scholarly journals The positive solutions of fractional differential equation with Riemann-Stieltjes integral boundary conditions

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2383-2394
Author(s):  
Xiaohan Zhang ◽  
Xiping Liu ◽  
Mei Jia ◽  
Haoliang Chen
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Stieltjes Integral ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
Ordered Banach Spaces

In this paper, we study a class of fractional differential equations with Riemann-Stieltjes integral boundary conditions. The existence and uniqueness of positive solutions for the boundary value problem are obtained via the use of fixed point theorems on cones in partially ordered Banach spaces. Many of the multi-point and integral boundary value problems studied previously studied are also included in our results.

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