scholarly journals On The Initial Value Problem For Fractional Volterra Integrodifferential Equations With A Caputo - Fabrizio Derivative

2021 ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Nguyen Anh Tuan ◽  
Donal O’regan ◽  
Vo Viet Tri
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Source Term ◽  
Main Tool ◽  
Integrodifferential Equations ◽  
Banach Fixed Point Theorem ◽  
Initial Value ◽  
Locally Lipschitz ◽  
Source Case ◽  
Well Posed

In this paper, time fractional integrodifferential equations with the Caputo - Fabrizio type derivative will be considered. In the case of a globally Lipschitz source term we obtain a global well - posed result on $\R^N$ for our problem. For the locally Lipschitz source case, we present existence and uniqueness and a finite time blow result for the solution. Our main tool is the Banach fixed point theorem and we extend  a  recent  paper of N.H. Tuan and Y. Zhou.

scholarly journals Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Tianlong Shen ◽  
Jianhua Huang ◽  
Jin Li
Keyword(s):  
Fixed Point ◽  
Diffusion Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Banach Fixed Point Theorem ◽  
Fractional Operator ◽  
Initial Value ◽  
Delayed Reaction

The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays.

Exponential Stability Estimate of Fully Nonlinear Aceive Equation by Boundary Control

2011 ◽  
Vol 467-469 ◽  
pp. 1078-1083
Author(s):  
Dian Chen Lu ◽  
Ruo Yu Zhu
Keyword(s):  
Fixed Point ◽  
Exponential Stability ◽  
Dispersion Equation ◽  
Boundary Control ◽  
Existence And Uniqueness ◽  
Stability Estimate ◽  
Banach Fixed Point Theorem ◽  
Operator Semigroups ◽  
Fully Nonlinear ◽  
Well Posed

The well-posed problem for the fully nonlinear Aceive diffusion and dispersion equation on the domain [0, 1] is investigated by using boundary control. The existence and uniqueness of the solutions with the help of the Banach fixed point theorem and the theory of operator semigroups are verified. By using some inequalities and integration by parts, the exponential stability of the fully nonlinear Aceive diffusion and dispersion equation with the designed boundary feedback is also proved.

scholarly journals EXISTENCE OF MONOTONIC ASYMPTOTICALLY CONSTANT SOLUTIONS FOR SECOND ORDER DIFFERENTIAL EQUATIONS

2007 ◽  
Vol 49 (3) ◽  
pp. 515-523 ◽  
Author(s):  
CRISTÓBAL GONZÁLEZ ◽  
ANTONIO JIMÉNEZ-MELADO
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Main Tool ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Second Order Differential Equations ◽  
Image Position

AbstractStarting from results of Dubé and Mingarelli, Wahlén, and Ehrström, who give conditions that ensure the existence and uniqueness of nonnegative nondecreasing solutions asymptotically constant of the equation we have been able to reduce their hypotheses in order to obtain the same existence results, at the expense of losing the uniqueness part. The main tool they used is the Banach Fixed Point Theorem, while ours has been the Schauder Fixed Point Theorem together with one version of the Arzelà-Ascoli Theorem.

scholarly journals The analysis of some special results of a Lasota–Wazewska model with mixed variable delays

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ramazan Yazgan ◽  
Osman Tunç
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Banach Fixed Point Theorem ◽  
Time Varying ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Variable Delays ◽  
Pseudo Almost Periodic ◽  
Mixed Variable

AbstractThis study is about getting some conditions that guarantee the existence and uniqueness of the weighted pseudo almost periodic (WPAP) solutions of a Lasota–Wazewska model with time-varying delays. Some adequate conditions have been obtained for the existence and uniqueness of the WPAP solutions of the Lasota–Wazewska model, which we dealt with using some differential inequalities, the WPAP theory, and the Banach fixed point theorem. Besides, an application is given to demonstrate the accuracy of the conditions of our main results.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

THE INITIAL VALUE PROBLEM FOR THE DEEP BÉNARD CONVECTION EQUATIONS WITH DATA IN Lq

1996 ◽  
Vol 06 (02) ◽  
pp. 269-277 ◽  
Author(s):  
Z. CHARKI
Keyword(s):  
Fixed Point ◽  
Initial Value Problem ◽  
Existence And Uniqueness ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Bénard Convection ◽  
Benard Convection ◽  
Point Argument

A fixed point argument is used to prove the existence and uniqueness of solutions for the unsteady deep Bénard convection equations in [Formula: see text] for [Formula: see text].

scholarly journals Existence, Uniqueness, and Approximation for Solutions of a Functional-integral Equation in Lp Spaces

2019 ◽  
Vol 20 (3) ◽  
pp. 403
Author(s):  
Suzete M Afonso ◽  
Juarez S Azevedo ◽  
Mariana P. G. Da Silva ◽  
Adson M Rocha
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
Functional Integral ◽  
Successive Approximation Method ◽  
Banach Fixed Point Theorem ◽  
Numerical Examples ◽  
Lp Spaces ◽  
Chebyshev Quadrature

In this work we consider the general functional-integral equation: \begin{equation*}y(t) = f\left(t, \int_{a}^{b} k(t,s)g(s,y(s))ds\right), \qquad t\in [a,b],\end{equation*}and give conditions that guarantee existence and uniqueness of solution in $L^p([a,b])$, with {$1<p<\infty$}.We use  Banach Fixed Point Theorem and employ the successive approximation method and Chebyshev quadrature for approximating the values of integrals. Finally, to illustrate the results of this work, we provide some numerical examples.

scholarly journals BANACH FIXED POINT THEOREM ON ORTHOGONAL CONE METRIC SPACES

2021 ◽  
pp. 1239
Author(s):  
Zeinab Eivazi Damirchi Darsi Olia ◽  
Madjid Eshaghi Gordji ◽  
Davood Ebrahimi Bagha
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Uniqueness Of Solution ◽  
Banach Fixed Point Theorem ◽  
Cone Metric Spaces ◽  
Cone Metric

In this paper, we introduce new concept of orthogonal cone metric spaces. We stablish new versions of fixed point theorems in incomplete orthogonal cone metric spaces. As an application, we show the existence and uniqueness of solution of the periodic boundry value problem.

scholarly journals The Neutral Stochastic Integrodifferential Equations with Jumps

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Diem Dang Huan
Keyword(s):  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Mild Solutions ◽  
Integrodifferential Equations ◽  
Poisson Jumps ◽  
Initial Value ◽  
Carathéodory Conditions ◽  
Global And Local ◽  
Continuous Dependence Of Solutions

We study the existence and uniqueness of mild solutions for neutral stochastic integrodifferential equations with Poisson jumps under global and local Carathéodory conditions on the coefficients by means of the successive approximation. Furthermore, we give the continuous dependence of solutions on the initial value. Finally, an example is provided to illustrate the effectiveness of the obtained results.

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