scholarly journals Variational Methods for an Impulsive Fractional Differential Equations with Derivative Term

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 880
Author(s):  
Yulin Zhao ◽  
Jiafa Xu ◽  
Haibo Chen
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Iterative Methods ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Technical Approach ◽  
Impulsive Fractional Differential Equations ◽  
Derivative Term ◽  
Fractional Differential

This paper is devoted to studying the existence of solutions to a class of impulsive fractional differential equations with derivative dependence. The used technical approach is based on variational methods and iterative methods. In addition, an example is given to demonstrate the main results.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations withp-Laplacian Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Ilkay Yaslan Karaca ◽  
Fatma Tokmak
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Laplacian Operator ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

This paper studies the existence of solutions for a nonlinear boundary value problem of impulsive fractional differential equations withp-Laplacian operator. Our results are based on some standard fixed point theorems. Examples are given to show the applicability of our results.

scholarly journals On the Existence of Solutions for Impulsive Fractional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yongliang Guan ◽  
Zengqin Zhao ◽  
Xiuli Lin
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solution ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Global Bifurcation ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We are concerned with a type of impulsive fractional differential equations attached with integral boundary conditions and get the existence of at least one positive solution via global bifurcation techniques.

scholarly journals Solutions for Impulsive Fractional Differential Equations via Variational Methods

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Peiluan Li ◽  
Hui Wang ◽  
Zheqing Li
Keyword(s):  
Differential Equations ◽  
Variational Methods ◽  
Boundary Value Problems ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Critical Points ◽  
Existence Results ◽  
Fractional Order Differential Equations ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We investigate the boundary value problems of impulsive fractional order differential equations. First, we obtain the existence of at least one solution by the minimization result of Mawhin and Willem. Then by the variational methods and a very recent critical points theorem of Bonanno and Marano, the existence results of at least triple solutions are established. At last, two examples are offered to demonstrate the application of our main results.

A new method for converting boundary value problems for impulsive fractional differential equations to integral equations and its applications

2017 ◽  
Vol 8 (1) ◽  
pp. 386-454 ◽  
Author(s):  
Yuji Liu
Keyword(s):  
Differential Equations ◽  
Boundary Value Problems ◽  
Fractional Differential Equations ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Impulsive Fractional Differential Equations ◽  
Periodic Boundary Value Problems ◽  
Fractional Differential

Abstract In this paper, we present a new method for converting boundary value problems of impulsive fractional differential equations to integral equations. Applications of this method are given to solve some types of anti-periodic boundary value problems for impulsive fractional differential equations. Firstly by using iterative method, we prove existence and uniqueness of solutions of Cauchy problems of differential equations involving Caputo fractional derivative, Riemann–Liouville and Hadamard fractional derivatives with order {q\in(0,1)} , see Theorem 2, Theorem 4, Theorem 6 and Theorem 8. Then we obtain exact expression of piecewise continuous solutions of these fractional differential equations see Theorem 1, Theorem 2, Theorem 3 and Theorem 4. Finally, four classes of integral type anti-periodic boundary value problems of singular fractional differential equations with impulse effects are proposed. Sufficient conditions are given for the existence of solutions of these problems. See Theorems 4.1–4.4. We allow the nonlinearity {p(t)f(t,x)} in fractional differential equations to be singular at {t=0,1} and be involved a super-linear and sub-linear term. The analysis relies on Schaefer’s fixed point theorem. In order to avoid misleading readers, we correct the results in [28] and [65]. We establish sufficient conditions for the existence of solutions of an anti-periodic boundary value problem for impulsive fractional differential equation. The results in [68] are complemented. The results in [81] are corrected. See Lemma 5.1, Lemma 5.7, Lemma 5.10 and Lemma 5.13.

scholarly journals Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations of Orderα∈(2,3]with Nonlocal Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-26 ◽  
Author(s):  
Lihong Zhang ◽  
Guotao Wang ◽  
Guangxing Song
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Nonlocal Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

We investigate the existence and uniqueness of solutions to the nonlocal boundary value problem for nonlinear impulsive fractional differential equations of orderα∈(2,3]. By using some well-known fixed point theorems, sufficient conditions for the existence of solutions are established. Some examples are presented to illustrate the main results.

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