Zhu, Jianbo Fu, Xianlong
Published in
Mathematica Slovaca

In this work, making use of the theory of resolvent operators and Banach fixed point theorem, we first discuss the existence and regularity of mild solutions for neutral partial functional integro-differential equations with infinite delay. We assume that the linear part of the considered equation generates a resolvent operator and the nonlinear fu...

Asker, Hussein K.
Published in
Journal of Systems Science and Information

In this work, neutral stochastic functional differential equations with infinite delay (NSFD-EwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space Cr under the local weak monotone condition, the weak coercivity condition and the global cond...

Wang, Chao Agarwal, Ravi P. O’Regan, Donal
Published in
Mathematica Slovaca

In this paper, by using the concept of changing-periodic time scales and composition theorem of time scales introduced in 2015, we establish a local phase space for functional dynamic equations with infinite delay (FDEID) on an arbitrary time scale with a bounded graininess function μ. Through Krasnoseľskiĭ’s fixed point theorem, some sufficient co...

Abbas, Saïd Benchohra, Mouffak
Published in
Mathematica Slovaca

In this paper, we shall present some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with not instantaneous impulses and state-dependent delay in Banach spaces. Some examples are also provided to illustrate our results.

Yan, Zuomao Jia, Xiumei
Published in
International Journal of Control, Automation and Systems

In this paper, we establish the existence of optimal controls of systems governed by a class of fractional impulsive partial neutral stochastic integro-differential systems with infinite delay in a Hilbert space. The approaches used are fixed point theorem, stochastic analysis theory, and approximation technique combined with properties of the solu...

Bao, Haibo Cao, Jinde
Published in
Advances in Difference Equations

This paper addresses a class of fractional stochastic impulsive neutral functional differential equations with infinite delay which arise from many practical applications such as viscoelasticity and electrochemistry. Using fractional calculations, fixed point theorems and the stochastic analysis technique, sufficient conditions are derived to ensur...

Ezzinbi, K. Miraoui, M. Rebey, A.
Published in
Mediterranean Journal of Mathematics

The aim of this work was to study the existence and uniqueness of μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu}$$\end{document}-pseudo almost periodic solution...

Afonso, Suzete M. Furtado, Andre L.

In this work, we establish the existence and uniqueness of antiperiodic solution for a class of nth-order functional differential equations with infinite delay. The main tool in our study is the coincidence degree theory. An example is presented to illustrate the results obtained.

Shukla, A. Sukavanam, N. Pandey, D. N.
Published in
Mediterranean Journal of Mathematics

The objective of this paper is to present some sufficient conditions for approximate controllability of semilinear fractional control system of order α∈(1,2]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odd...

Chen, Fengde Xie, Xiangdong Wang, Haina
Published in
Journal of Systems Science and Complexity

A competition model of plankton allelopathy with infinite delay is considered in this paper. By using an iterative method, the global stability of the interior equilibrium point of the system is investigated. The result shows that for this system, delay and toxic substances are harmless for the stability of the interior equilibrium point.