scholarly journals Existence of Solutions for Boundary Value Problems of Vibration Equation with Fractional Derivative

2019 ◽  
Vol 07 (05) ◽  
pp. 1067-1076
Author(s):  
Nan Yao ◽  
Zeyu Luo
Keyword(s):  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Vibration Equation

scholarly journals Existence of Solutions for Fractional Boundary Value Problems with a Quadratic Growth of Fractional Derivative

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yaning Li ◽  
Quanguo Zhang ◽  
Baoyan Sun
Keyword(s):  
Fractional Derivative ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Boundary Problem ◽  
Linear Growth ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Quadratic Growth ◽  
Fractional Boundary Value Problems

In this paper, we deal with two fractional boundary value problems which have linear growth and quadratic growth about the fractional derivative in the nonlinearity term. By using variational methods coupled with the iterative methods, we obtain the existence results of solutions. To the best of the authors’ knowledge, there are no results on the solutions to the fractional boundary problem which have quadratic growth about the fractional derivative in the nonlinearity term.

scholarly journals Sufficient conditions for the existence of solutions for boundary value problems for fractional differential equations

2020 ◽  
Author(s):  
Abdulkadir Dogan
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential ◽  
Set Up

In this article, we set up adequate circumstances for the existence of solutions for boundary value problems of fractional differential equations including the Caputo fractional derivative and nonlocal conditions.

scholarly journals Existence of Solutions for a Periodic Boundary ValueProblem with Impulse and Fractional Derivative Dependence

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Yaohong Li ◽  
Yongqing Wang ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Growth Conditions ◽  
Boundary Values ◽  
Periodic Boundary Value Problems

In this paper, we present some theorems on impulsive periodic boundary value problems with fractional derivative dependence. In particular, we discuss the existence of solutions of a class of fractional-order impulsive periodic boundary values with nonlinear terms and impulsive terms satisfying certain growth conditions. Three examples are provided to illustrate our results.

Boundary Value Problems for Fractional Differential Equations

2009 ◽  
Vol 16 (3) ◽  
pp. 401-411 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Samira Hamani
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Caputo Fractional Derivative ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Fractional Differential

Abstract The sufficient conditions are established for the existence of solutions for a class of boundary value problems for fractional differential equations involving the Caputo fractional derivative.

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 Non-Instantaneous Impulsive Boundary Value Problems Containing Caputo Fractional Derivative of a Function with Respect to Another Function and Riemann–Stieltjes Fractional Integral Boundary Conditions

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 130
Author(s):  
Suphawat Asawasamrit ◽  
Yasintorn Thadang ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Caputo Fractional Derivative ◽  
Fractional Integral ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Uniqueness Results ◽  
Nonlinear Alternative

In the present article we study existence and uniqueness results for a new class of boundary value problems consisting by non-instantaneous impulses and Caputo fractional derivative of a function with respect to another function, supplemented with Riemann–Stieltjes fractional integral boundary conditions. The existence of a unique solution is obtained via Banach’s contraction mapping principle, while an existence result is established by using Leray–Schauder nonlinear alternative. Examples illustrating the main results are also constructed.

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