scholarly journals Impulsive functional-differential equations with nonlocal conditions

2002 ◽  
Vol 29 (5) ◽  
pp. 251-256 ◽  
Author(s):  
Haydar Akça ◽  
Abdelkader Boucherif ◽  
Valéry Covachev
Keyword(s):  
Continuous Dependence ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Semigroup Of Operators ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

The existence, uniqueness, and continuous dependence of a mild solution of an impulsive functional-differential evolution nonlocal Cauchy problem in general Banach spaces are studied. Methods of fixed point theorems, of aC0semigroup of operators and the Banach contraction theorem are applied.

scholarly journals On a mild solution of a semilinear functional-differential evolution nonlocal problem

1997 ◽  
Vol 10 (3) ◽  
pp. 265-271 ◽  
Author(s):  
Ludwik Byszewski ◽  
Haydar Akca
Keyword(s):  
Differential Evolution ◽  
Mild Solution ◽  
Continuous Dependence ◽  
Nonlocal Problem ◽  
Semigroup Of Operators ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

The existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear functional-differential evolution equation in a general Banach space are studied. Methods of a C0 semigroup of operators and the Banach contraction theorem are applied. The result obtained herein is a generalization and continuation of those reported in references [2-8].

scholarly journals On Some Qualitative Properties of Mild Solutions of Nonlocal Semilinear Functional Differential Equations

2014 ◽  
Vol 47 (4) ◽  
Author(s):  
Rupali S. Jain ◽  
M. B. Dhakne
Keyword(s):  
Differential Equations ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Functional Differential Equations ◽  
Qualitative Properties ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Banach Contraction Theorem ◽  
Equations With Delay

AbstractIn the present paper, we investigate the qualitative properties such as existence, uniqueness and continuous dependence on initial data of mild solutions of first and second order nonlocal semilinear functional differential equations with delay in Banach spaces. Our analysis is based on semigroup theory and modified version of Banach contraction theorem.

scholarly journals Existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem

1999 ◽  
Vol 12 (1) ◽  
pp. 91-97 ◽  
Author(s):  
Ludwik Byszewski
Keyword(s):  
Cauchy Problem ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Special Kind ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Picard Method ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

The aim of this paper is to investigate the existence and uniqueness of a classical solution to a functional-differential abstract nonlocal Cauchy problem in a general Banach space. For this purpose, a special kind of a mild solution is introduced and the Banach contraction theorem and a modified Picard method are applied.

scholarly journals Existence and uniqueness of solutions of a semilinear functional-differential evolution nonlocal Cauchy problem

2000 ◽  
Vol 13 (2) ◽  
pp. 171-179
Author(s):  
Katarzyna Kolodziej
Keyword(s):  
Cauchy Problem ◽  
Differential Evolution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Uniqueness Of Solutions ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Functional Differential ◽  
Nonlocal Cauchy Problem ◽  
Banach Contraction Theorem

Two theorems about the existence and uniqueness of mild and classical solutions of a semilinear functional-differential evolution nonlocal Cauchy problem in a general Banach space are proved. Methods of semigroups and the Banach contraction theorem are applied.

scholarly journals Existence Results for Semilinear Functional Differential System with Nonlocal Conditions

2018 ◽  
Vol 8 (10S) ◽  
pp. 237-241
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Fixed Point Theorems ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Abstract Space ◽  
Functional Differential ◽  
Functional Differential System

In this paper, sufficient conditions are given for the existence of partial functional differential equations with nonlocal conditions in an abstract space with the help of the fixed point theorems.

scholarly journals Existence results of noninstantaneous impulsive fractional integro-differential equation

2020 ◽  
Vol 53 (1) ◽  
pp. 373-384 ◽  
Author(s):  
Haribhai R. Kataria ◽  
Prakashkumar H. Patel ◽  
Vishant Shah
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Fixed Point ◽  
Semigroup Theory ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem

Abstract Existence of mild solution for noninstantaneous impulsive fractional order integro-differential equations with local and nonlocal conditions in Banach space is established in this paper. Existence results with local and nonlocal conditions are obtained through operator semigroup theory using generalized Banach contraction theorem and Krasnoselskii’s fixed point theorem, respectively. Finally, illustrations are added to validate derived results.

scholarly journals Functional Differential Inequalities with Unbounded Delay

2005 ◽  
Vol 12 (2) ◽  
pp. 237-254
Author(s):  
Zdzisław Kamont ◽  
Adam Nadolski
Keyword(s):  
Differential Inequality ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Classical Solutions ◽  
Differential Inequalities ◽  
Unbounded Delay ◽  
Several Variables ◽  
Functional Differential ◽  
Continuous Dependence Of Solutions

Abstract We prove that a function of several variables satisfying a functional differential inequality with unbounded delay can be estimated by a solution of a suitable initial problem for an ordinary functional differential equation. As a consequence of the comparison theorem we obtain a Perron-type uniqueness result and a result on continuous dependence of solutions on given functions for partial functional differential equations with unbounded delay. We consider classical solutions on the Haar pyramid.

scholarly journals The Existence of Solutions for Boundary Value Problem of Fractional Functional Differential Equations with Delay

2018 ◽  
Vol 228 ◽  
pp. 01005
Author(s):  
Mengrui Xu ◽  
Yanan Li ◽  
Yige Zhao ◽  
Shurong Sun
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Contraction Mapping Principle ◽  
Alternative Theorem ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

A class of boundary value problem for fractional functional differential equation with delay $ \left\{ {\begin{array}{*{20}c} {^{C} D^{\sigma } \omega (t) = f(t,\omega _{t} ),t \in [0,\zeta ],} \\ {\omega (0) = 0,\,\omega ^{\prime}(0) = 0,\,\omega ^{\prime\prime}(\zeta ) = 1,} \\ \end{array} } \right. $ is studied, where $ 2 < \sigma \le 3,\,\,^{c} D^{\sigma } $ devote standard Caputo fractional derivative. In this article, three new criteria on existence and uniqueness of solution are obtained by Banach contraction mapping principle, Schauder fixed point theorem and nonlinear alternative theorem.

Controllability results of fractional integro-differential equation with non-instantaneous impulses on time scales

2020 ◽  
Author(s):  
Vipin Kumar ◽  
Muslim Malik
Keyword(s):  
Differential Equation ◽  
Functional Analysis ◽  
Time Scales ◽  
Linear Functional ◽  
Integro Differential Equation ◽  
Numerical Example ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem ◽  
Different Time Scales

Abstract In this work, we investigate the controllability results of a fractional integro-differential equation with non-instantaneous impulses on time scales. Banach contraction theorem and the non-linear functional analysis have been used to establish these results. In support, a numerical example with simulation for different time scales is given to validate the obtained analytical outcomes.

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