scholarly journals Quasistatic Elastic Contact with Adhesion

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Boudjemaa Teniou ◽  
Sabrina Benferdi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Elastic Contact ◽  
Rigid Foundation ◽  
Mechanical Problem ◽  
Quasistatic Process ◽  
Variational Study ◽  
Nonlinear Elastic

The aim of this paper is the variational study of the contact with adhesion between an elastic material and a rigid foundation in the quasistatic process where the deformations are supposed to be small. The behavior of this material is modelled by a nonlinear elastic law and the contact is modelled with Signorini's conditions and adhesion. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the mechanical problem, and we prove the existence and uniqueness of the weak solution using a theorem on variational inequalities, the theorem of Cauchy-Lipschitz, a lemma of Gronwall, as well as the fixed point of Banach.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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 of the Mild Solutions for Impulsive Fractional Equations with Infinite Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Jaydev Dabas ◽  
Archana Chauhan ◽  
Mukesh Kumar
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Order ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Fractional Equations ◽  
Evolution Differential Equation

This paper is concerned with the existence and uniqueness of a mild solution of a semilinear fractional-order functional evolution differential equation with the infinite delay and impulsive effects. The existence and uniqueness of a mild solution is established using a solution operator and the classical fixed-point theorems.

scholarly journals Existence and Uniqueness of Solutions for Coupled Impulsive Fractional Pantograph Differential Equations with Antiperiodic Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Karim Guida ◽  
Lahcen Ibnelazyz ◽  
Khalid Hilal ◽  
Said Melliani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Fractional Differential ◽  
Banach’S Contraction Principle

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based on Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Two examples are given in the last part to support our study.

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 On the Theory of ψ-Hilfer Nonlocal Cauchy Problem

2021 ◽  
pp. 161-177
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Fixed Point ◽  
Constant Coefficient ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Representation Formula ◽  
Qualitative Properties ◽  
Fractional Differential ◽  
Nonlocal Cauchy Problem

In this paper, we derive the representation formula of the solution for ψ-Hilfer fractional differential equation with constant coefficient in the form of Mittag-Leffler function by using Picard’s successive approximation. Moreover, by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer, we introduce new results of some qualitative properties of solution such as existence and uniqueness. The generalized Gronwall inequality lemma is used in analyze Eα -Ulam-Hyers stability. Finally, one example to illustrate the obtained results

scholarly journals Existence and Uniqueness with Ulam Stability study of the solution for a class of Caputo fractional integro-differential equation with mixed conditions

2021 ◽  
Author(s):  
ABDELLOUAHAB Naimi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Stability Study ◽  
Ulam Stability ◽  
Differential Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Stability Results

In this article we show the existence, uniqueness and Ulam stability results of the solution for a class of a nonlinear Caputo fractional integro-differential problem with mixed conditions. we use three fixed point theorems to proof the existence and uniqueness results. By the results obtained, the reasons for the Ulam stability are verified. An example proposed to illustrate our main results.

scholarly journals Existence and Uniqueness for the Controllability of a Dynamical System

2019 ◽  
pp. 168-173
Author(s):  
Eli Innocent Cleopas ◽  
Godspower C. Abanum
Keyword(s):  
Dynamical System ◽  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Integro Differential Equation ◽  
Darbo’S Fixed Point Theorem

In this paper, we consider the existence and uniqueness for the controllability of a dynamical system. Here, measure of non-compactness of set was employed to examine the conditions for darbo’s fixed point theorem which is used to established the existence and uniqueness solution for nonlinear integro-differential equation with implicit derivatives.

scholarly journals Positive Solutions of Nonlinear Fractional Differential Equations with Integral Boundary Value Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
J. Caballero ◽  
I. Cabrera ◽  
K. Sadarangani
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Partially Ordered Sets ◽  
Ordered Sets ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Fractional Differential

We investigate the existence and uniqueness of positive solutions of the following nonlinear fractional differential equation with integral boundary value conditions, , , where , and is the Caputo fractional derivative and is a continuous function. Our analysis relies on a fixed point theorem in partially ordered sets. Moreover, we compare our results with others that appear in the literature.

scholarly journals Existence and Uniqueness Results of Volterra–Fredholm Integro-Differential Equations via Caputo Fractional Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ameth Ndiaye ◽  
Fulgence Mansal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Ulam Stability ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
The Fixed Point Theorem ◽  
Banach Principle ◽  
Stability Of The Solution

In this paper, we study a Volterra–Fredholm integro-differential equation. The considered problem involves the fractional Caputo derivatives under some conditions on the order. We prove an existence and uniqueness analytic result by application of the Banach principle. Then, another result that deals with the existence of at least one solution is delivered, and some sufficient conditions for this result are established by means of the fixed point theorem of Schaefer. Ulam stability of the solution is discussed before including an example to illustrate the results of the proposal.

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