Existence Results for Integro-Differential Equations with Reflection

We consider a class of nonautonomous cellular neural networks (CNNs) with mixed delays, to study the solutions of these systems which are type pseudo almost periodicity. Using general measure theory and the Mittag-Leffler function, we obtain the existence of unique solutions for cellular neural equations and investigate the Mittag-Leffler stability and attractiveness of pseudo almost periodic functions. We also present numerical examples to illustrate the application of our results.

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“…We can derive the Mittag-Leffler attractiveness from the Mittag-Leffler stability; for more details, see [21][22][23][24][25][26][27].…”

Section: Preliminariesmentioning

confidence: 99%

Mittag-Leffler Stability and Attractiveness of Pseudo Almost Periodic Solutions for Delayed Cellular Neural Networks

Eidinejad

Saadati

Repovš

2022

Journal of Function Spaces

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Pseudo Almost Periodic Solution for Some Differential Equations with Piecewise Constant Argument and Applications

Arfa,

Assel,

Miraoui

2024

Complex Anal. Oper. Theory

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Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability

Sarsenbi,

Sarsenbi

2023

MATH

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<abstract> <p>We consider the two-point boundary value problems for a nonlinear one-dimensional second-order differential equation with involution in the second derivative and in lower terms. The questions of existence and uniqueness of the classical solution of two-point boundary value problems are studied. The definition of the Green's function is generalized for the case of boundary value problems for the second-order linear differential equation with involution, indicating the points of discontinuities and the magnitude of discontinuities of the first derivative. Uniform estimates for the Green's function of the linear part of boundary value problems are established. Using the contraction mapping principle and the Schauder fixed point theorem, theorems on the existence and uniqueness of solutions to the boundary value problems are proved. The results obtained in this paper cover the boundary value problems for one-dimensional differential equations with and without involution in the lower terms.</p> </abstract>

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Existence Results for Integro-Differential Equations with Reflection

Cited by 3 publications

References 25 publications

Mittag-Leffler Stability and Attractiveness of Pseudo Almost Periodic Solutions for Delayed Cellular Neural Networks

Mittag-Leffler Stability and Attractiveness of Pseudo Almost Periodic Solutions for Delayed Cellular Neural Networks

Pseudo Almost Periodic Solution for Some Differential Equations with Piecewise Constant Argument and Applications

Boundary value problems for a second-order differential equation with involution in the second derivative and their solvability

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