Existence and Uniqueness Theorem of the Solution to a Class of Nonlinear Nabla Fractional Difference System with a Time Delay

2018 ◽  
Vol 15 (6) ◽  
Author(s):  
Churong Chen ◽  
Baoguo Jia ◽  
Xiang Liu ◽  
Lynn Erbe
Keyword(s):  
Time Delay ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Difference System ◽  
Existence And Uniqueness Theorem ◽  
Fractional Difference

scholarly journals A CLASS OF QUASISTATIC CONTACT PROBLEMS FOR VISCOELASTIC MATERIALS WITH NONLOCAL COULOMB FRICTION AND TIME-DELAY

2014 ◽  
Vol 19 (4) ◽  
pp. 491-508 ◽  
Author(s):  
Si-sheng Yao ◽  
Nan-jing Huang
Keyword(s):  
Mathematical Model ◽  
Variational Inequality ◽  
Time Delay ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Variational Formulation ◽  
Frictional Contact ◽  
Contact Problems ◽  
Existence And Uniqueness Theorem ◽  
Differential Variational Inequality

In this paper, a mathematical model which describes the explicit time dependent quasistatic frictional contact problems is introduced and studied. The material behavior is described with a nonlinear viscoelastic constitutive law with time-delay and the frictional contact is modeled with nonlocal Coulomb boundary conditions. A variational formulation of the mathematical model is given, which is called a quasistatic integro-differential variational inequality. Using the Banach's fixed point theorem, an existence and uniqueness theorem of the solution for the quasistatic integro-differential variational inequality is proved under some suitable assumptions. As an application, an existence and uniqueness theorem of the solution for the dual variational formulation is also given.

scholarly journals Asymptotically almost automorphic solutions of differential equations with piecewise constant argument

2017 ◽  
Vol 15 (1) ◽  
pp. 595-610
Author(s):  
Hui-Sheng Ding ◽  
Shun-Mei Wan
Keyword(s):  
Differential Equations ◽  
Uniqueness Theorem ◽  
Systematic Study ◽  
Existence And Uniqueness ◽  
Difference System ◽  
Existence And Uniqueness Theorem ◽  
Piecewise Constant ◽  
Almost Automorphic ◽  
Piecewise Constant Argument ◽  
Constant Argument

Abstract This paper is concerned with the existence and uniqueness of asymptotically almost automorphic solutions to differential equations with piecewise constant argument. To study that, we first introduce several notions about asymptotically almost automorphic type functions and obtain some properties of such functions. Then, on the basis of a systematic study on the associated difference system, the existence and uniqueness theorem is established. Compared with some earlier results, we do not assume directly that the Green’s function is a Bi-almost automorphic type function.

scholarly journals Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

Sign in / Sign up

Export Citation Format

Share Document