scholarly journals Existence and Attractivity Results for Coupled Systems of Nonlinear Volterra–Stieltjes Multidelay Fractional Partial Integral Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Naima Hamidi ◽  
Gaston N’Guérékata
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Coupled Systems ◽  
Schauder’S Fixed Point Theorem ◽  
Integral System ◽  
Schauder's Fixed Point Theorem ◽  
Globally Attractive

We are concerned with some existence and attractivity results of a coupled fractional Riemann–Liouville–Volterra–Stieltjes multidelay partial integral system. We prove the existence of solutions using Schauder’s fixed point theorem; then we show that the solutions are uniformly globally attractive.

scholarly journals The Solvability and Optimal Controls for Some Fractional Impulsive Equations of Order1< α<2

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xianghu Liu ◽  
Zhenhai Liu ◽  
Maojun Bin
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Schauder’S Fixed Point Theorem ◽  
Sufficient Condition ◽  
Optimal Controls ◽  
Schauder's Fixed Point Theorem ◽  
Gronwall’S Inequality ◽  
Impulsive Equations

We study the existence of solutions and optimal controls for some fractional impulsive equations of order1< α<2. By means of Gronwall’s inequality and Leray-Schauder’s fixed point theorem, the sufficient condition for the existence of solutions and optimal controls is presented. Finally, an example is given to illustrate our main results.

scholarly journals A Note on Periodic Solutions of Second Order Nonautonomous Singular Coupled Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Zhongwei Cao ◽  
Chengjun Yuan ◽  
Daqing Jiang ◽  
Xiaowei Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Second Order ◽  
Coupled Systems ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Periodic Solutions

We establish the existence of periodic solutions of the second order nonautonomous singular coupled systemsx′′+a1(t)x=f1(t,y(t))+e1(t)for a.e.t∈[0,T],y′′+a2(t)y=f2(t,x(t))+e2(t)for a.e.t∈[0,T]. The proof relies on Schauder's fixed point theorem.

scholarly journals Existence of Solutions for a Quasilinear System with Gradient Terms

2021 ◽  
pp. 239-246
Author(s):  
Leandro S. Tavares
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Growth Conditions ◽  
Quasilinear System ◽  
Schauder’S Fixed Point Theorem ◽  
Laplacian Operator ◽  
Schauder's Fixed Point Theorem

In this paper, it is considered the existence of solutions for a quasilinear system involving the p-Laplacian operator and gradient terms. The approach is based on sub-supersolution arguments and the Schauder's Fixed Point Theorem. The results in this paper allow to consider several growth conditions in the gradient and complete some recent contributions.

scholarly journals A Periodic Solution of the Generalized Forced Liénard Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Zahra Goodarzi ◽  
Abdolrahman Razani
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Liénard Equation ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Lienard Equation

We consider the generalized forced Liénard equation as follows:(ϕp(x′))′+(f(x)+k(x)x′)x′+g(x)=p(t)+s. By applying Schauder's fixed point theorem, the existence of at least one periodic solution of this equation is proved.

scholarly journals Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Xinguang Zhang ◽  
Cuiling Mao ◽  
Yonghong Wu ◽  
Hua Su
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Differential System ◽  
Point Theorem ◽  
Schauder’S Fixed Point Theorem ◽  
Schauder's Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Two Parameters

We establish the existence of positive solutions to a class of singular nonlocal fractional order differential system depending on two parameters. Our methods are based on Schauder’s fixed point theorem.

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