scholarly journals Existence and Uniqueness of Positive Solutions for a Fractional Switched System

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhi-Wei Lv ◽  
Bao-Feng Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Constant Function ◽  
Switched System ◽  
Piecewise Constant Function ◽  
Piecewise Constant

We discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0,t∈J=[0,1]);(u(0)=u′′(0)=0,u(1)=∫01u(s) ds), whereDc0+αis the Caputo fractional derivative with2<α≤3,σ(t):J→{1,2,…,N}is a piecewise constant function depending ont, andℝ+=[0,+∞),  fi,gi∈C[J×ℝ+,ℝ+],i=1,2,…,N. Our results are based on a fixed point theorem of a sum operator and contraction mapping principle. Furthermore, two examples are also given to illustrate the results.

Existence and uniqueness of solutions of nonlinear fractional order problems via a fixed point theorem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Zahra Ahmadi ◽  
Rahmatollah Lashkaripour ◽  
Hamid Baghani ◽  
Shapour Heidarkhani
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Uniqueness Of Solutions ◽  
Order Problem ◽  
Krasnoselskii’S Fixed Point Theorem

AbstractIn this paper, we introduce an Caputo fractional high-order problem with a new boundary condition including two orders $\gamma \in \left({n}_{1}-1,{n}_{1}\right]$ and $\eta \in \left({n}_{2}-1,{n}_{2}\right]$ for any ${n}_{1},{n}_{2}\in \mathrm{&#x2115;}$. We deals with existence and uniqueness of solutions for the problem. The approach is based on the Krasnoselskii’s fixed point theorem and contraction mapping principle. Moreover, we present several examples to show the clarification and effectiveness.

scholarly journals Existence and uniqueness results for Ψ-fractional integro-differential equations with boundary conditions

2020 ◽  
Vol 107 (121) ◽  
pp. 145-155
Author(s):  
Devaraj Vivek ◽  
E.M. Elsayed ◽  
Kuppusamy Kanagarajan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

We study boundary value problems (BVPs for short) for the integro- differential equations via ?-fractional derivative. The results are obtained by using the contraction mapping principle and Schaefer?s fixed point theorem. In addition, we discuss the Ulam-Hyers stability.

scholarly journals Uniqueness of Positive Solutions for a Perturbed Fractional Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Chen Yang ◽  
Jieming Zhang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Point Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and uniqueness of positive solutions for the following nonlinear perturbed fractional two-point boundary value problem:D0+αu(t)+f(t,u,u',…,u(n-2))+g(t)=0, 0<t<1, n-1<α≤n, n≥2,u(0)=u'(0)=⋯=u(n-2)(0)=u(n-2)(1)=0, whereD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on a fixed-point theorem of generalized concave operators. An example is given to illustrate the main result.

scholarly journals Existence and Uniqueness of Positive Solutions for a Singular Fractional Three-Point Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
I. J. Cabrera ◽  
J. Harjani ◽  
K. B. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Boundary Value ◽  
Point Boundary ◽  
Ordered Metric Spaces ◽  
Liouville Derivative

We investigate the existence and uniqueness of positive solutions for the following singular fractional three-point boundary value problemD0+αu(t)+f(t,u(t))=0, 0<t<1, u(0)=u′(0)=u′′(0)=0,u′′(1)=βu′′(η), where3<α≤4,D0+αis the standard Riemann-Liouville derivative andf:(0,1]×[0,∞)→[0,∞)withlim t→0+f(t,·)=∞(i.e.,fis singular att=0). Our analysis relies on a fixed point theorem in partially ordered metric spaces.

scholarly journals Existence-uniqueness of positive solutions to nonlinear impulsive fractional differential systems and optimal control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shu Song ◽  
Lingling Zhang ◽  
Bibo Zhou ◽  
Nan Zhang
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Mixed Monotone Operator ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Fractional Differential

Abstract In this thesis, we investigate a kind of impulsive fractional order differential systems involving control terms. By using a class of φ-concave-convex mixed monotone operator fixed point theorem, we obtain a theorem on the existence and uniqueness of positive solutions for the impulsive fractional differential equation, and the optimal control problem of positive solutions is also studied. As applications, an example is offered to illustrate our main results.

scholarly journals Maia type fixed point theorems for Ćirić-Prešić operators

2018 ◽  
Vol 10 (1) ◽  
pp. 18-31
Author(s):  
Margareta-Eliza Balazs
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Acta Math ◽  
Contraction Mapping Principle ◽  
Contraction Condition ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

Abstract The main aim of this paper is to obtain Maia type fixed point results for Ćirić-Prešić contraction condition, following Ćirić L. B. and Prešić S. B. result proved in [Ćirić L. B.; Prešić S. B. On Prešić type generalization of the Banach contraction mapping principle, Acta Math. Univ. Comenian. (N.S.), 2007, v 76, no. 2, 143–147] and Luong N. V. and Thuan N. X. result in [Luong, N. V., Thuan, N. X., Some fixed point theorems of Prešić-Ćirić type, Acta Univ. Apulensis Math. Inform., No. 30, (2012), 237–249]. We unified these theorems with Maia’s fixed point theorem proved in [Maia, Maria Grazia. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 1968 139–143] and the obtained results are proved is the present paper. An example is also provided.

scholarly journals Existence and Uniqueness of Positive Solutions to Nonlinear Second Order Impulsive Differential Equations with Concave or Convex Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Lingling Zhang ◽  
Chengbo Zhai
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Impulsive Differential Equations ◽  
Second Order ◽  
Point Boundary

Using a new fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to nonlinear two-point boundary value problems for second-order impulsive differential equations with concave or convex nonlinearities.

scholarly journals Uniqueness of Positive Solutions for a Class of Fourth-Order Boundary Value Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
J. Caballero ◽  
J. Harjani ◽  
K. Sadarangani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Boundary Value ◽  
Ordered Metric Spaces ◽  
Symmetric Positive Solution

The purpose of this paper is to investigate the existence and uniqueness of positive solutions for the following fourth-order boundary value problem: , , . Moreover, under certain assumptions, we will prove that the above boundary value problem has a unique symmetric positive solution. Finally, we present some examples and we compare our results with the ones obtained in recent papers. Our analysis relies on a fixed point theorem in partially ordered metric spaces.

scholarly journals Revisiting of some outstanding metric fixed point theorems via E-contraction

2018 ◽  
Vol 26 (3) ◽  
pp. 73-98
Author(s):  
Andreea Fulga ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Fixed Point Theorems ◽  
Contractive Mapping ◽  
Contraction Mapping Principle ◽  
Contraction Mappings ◽  
Banach Contraction ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

AbstractIn this paper, we introduce the notion of α-ψ-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle.

scholarly journals Existence of Solutions for Integrodifferential Equations of Fractional Order with Antiperiodic Boundary Conditions

2009 ◽  
Vol 2009 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmed Alsaedi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Existence Of Solutions ◽  
Contraction Mapping Principle ◽  
Integrodifferential Equations ◽  
Krasnoselskii’S Fixed Point Theorem

We discuss the existence of solutions for a nonlinear antiperiodic boundary value problem of integrodifferential equations of fractional orderq∈(1,2]. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to establish the results.

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