scholarly journals Resonant Integral Boundary Value Problems for Caputo Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Wenjie Ma ◽  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
At Resonance ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

This paper deals with the following Caputo fractional differential equations with Riemann-Stieltjes integral boundary conditions Dc0+αut=ft,ut,u′t,u′′t,  t∈0,1,  u0=u′′0=0,  u1=∫01‍utdAt, where Dc0+α denotes the standard Caputo derivative, α∈(2,3]; ∫01x(t)dA(t) denotes the Riemann-Stieltjes integrals of x with respect to A. By mean of coincidence degree theory, we obtain the existence of solutions for the above fractional BVP at resonance. In the end, according to the main results, we give a typical example.

scholarly journals The Existence of Solutions to Integral Boundary Value Problems of Fractional Differential Equations at Resonance

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Yumei Zou ◽  
Guoping He
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Integral Boundary ◽  
At Resonance ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

This paper deals with the integral boundary value problems of fractional differential equations at resonance. By Mawhin’s coincidence degree theory, we present some new results on the existence of solutions for a class of differential equations of fractional order with integral boundary conditions at resonance. An example is also included to illustrate the main results.

scholarly journals Existence of Solutions for Fractional Differential Equations with p-Laplacian Operator and Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jingli Xie ◽  
Lijing Duan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Integral Boundary Conditions ◽  
Laplacian Operator ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Integral Boundary Value Problems ◽  
The Fixed Point Theorem

In this paper, we investigate a class of integral boundary value problems of fractional differential equations with a p-Laplacian operator. Existence of solutions is obtained by using the fixed point theorem, and an example is given to show the applicability of our main result.

scholarly journals A second order differential equation with generalized Sturm-Liouville integral boundary conditions at resonance

Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1437-1444 ◽  
Author(s):  
Zengji Du ◽  
Jian Yin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlinear Differential Equations ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Second Order ◽  
Integral Boundary ◽  
At Resonance ◽  
Sturm Liouville

By using Mawhin coincidence degree theory, we investigate the existence of solutions for a class of second order nonlinear differential equations with generalized Sturm-Liouville integral boundary conditions at resonance. The results extend some known conclusions of integral boundary value problem at resonance for nonlinear differential equations

scholarly journals The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yumei Zou ◽  
Lishan Liu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
At Resonance ◽  
Fractional Differential

A four-point coupled boundary value problem of fractional differential equations is studied. Based on Mawhin’s coincidence degree theory, some existence theorems are obtained in the case of resonance.

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 Existence of Solutions for Two-Point Boundary Value Problem of Fractional Differential Equations at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Hu ◽  
Shuqin Zhang ◽  
Ailing Shi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Point Boundary ◽  
At Resonance ◽  
Fractional Differential

We establish the existence results for two-point boundary value problem of fractional differential equations at resonance by means of the coincidence degree theory. Furthermore, a result on the uniqueness of solution is obtained. We give an example to demonstrate our results.

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