scholarly journals On resonant mixed Caputo fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Assia Guezane-Lakoud ◽  
Adem Kılıçman
Keyword(s):  
Differential Equation ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Caputo Fractional Derivatives ◽  
At Resonance ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Problem At Resonance

Abstract The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional derivatives. The proofs of the existence of solutions are mainly based on Mawhin’s coincidence degree theory. We provide an example to illustrate the main result.

scholarly journals The Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoling Han ◽  
Ting Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Of Solution ◽  
At Resonance ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory.

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 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 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.

PERIODIC BOUNDARY VALUE PROBLEM FOR FRACTIONAL DIFFERENTIAL EQUATION

2012 ◽  
Vol 23 (10) ◽  
pp. 1250100 ◽  
Author(s):  
ZHIGANG HU ◽  
WENBIN LIU ◽  
WENJUAN RUI
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Periodic Boundary Value Problem ◽  
Fractional Differential

In this paper, by using the coincidence degree theory, we consider periodic boundary value problem for fractional differential equation. A new result on the existence of solutions for above fractional boundary value problem is obtained.

scholarly journals Solvability of Some Nonlocal Fractional Boundary Value Problems at Resonance in Rn

2022 ◽  
Vol 6 (1) ◽  
pp. 25
Author(s):  
Yizhe Feng ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Interesting Point ◽  
State Variable ◽  
At Resonance ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

In this paper, the solvability of a system of nonlinear Caputo fractional differential equations at resonance is considered. The interesting point is that the state variable x∈Rn and the effect of the coefficient matrices matrices B and C of boundary value conditions on the solvability of the problem are systematically discussed. By using Mawhin coincidence degree theory, some sufficient conditions for the solvability of the problem are obtained.

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

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