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 Existence results for fractional neutral integro-differential systems with nonlocal condition through resolvent operators

2019 ◽  
Vol 27 (1) ◽  
pp. 107-124
Author(s):  
D. Mallika ◽  
D. Baleanu ◽  
S. Suganya ◽  
M. Mallika Arjunan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Resolvent Operators ◽  
Differential Systems ◽  
Banach Contraction ◽  
Krasnoselskii Fixed Point Theorem ◽  
The Banach Contraction Principle

Abstract The manuscript is primarily concerned with the new existence results for fractional neutral integro-differential equation (FNIDE) with nonlocal conditions (NLCs) in Banach spaces. Based on the Banach contraction principle and Krasnoselskii fixed point theorem (FPT) joined with resolvent operators, we develop the main results. Ultimately, an representation is also offered to demonstrate the accomplished theorem.

scholarly journals The Impulsive Neutral Integro-Differential Equations with Infinite Delay and Non-Instantaneous Impulses

2018 ◽  
Vol 7 (4.10) ◽  
pp. 694
Author(s):  
V. Usha ◽  
M. Mallika Arjunan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Semigroup Theory ◽  
Existence Results ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
The Fixed Point Theorem

In this manuscript, we work to accomplish the Krasnoselskii's fixed point theorem to analyze the existence results for an impulsive neutral integro-differential equations  with infinite delay and non-instantaneous impulses in Banach spaces. By deploying the fixed point theorem with semigroup theory, we developed the coveted outcomes.   

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.

scholarly journals On Some Fixed Point Results in E − Fuzzy Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Rachid Mecheraoui ◽  
Zoran D. Mitrović ◽  
Vahid Parvaneh ◽  
Hassen Aydi ◽  
Naeem Saleem
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Additional Condition ◽  
Metric Spaces ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
New Class ◽  
Contraction Theorem ◽  
Banach Contraction ◽  
Banach Contraction Theorem

In the existing literature, Banach contraction theorem as well as Meir-Keeler fixed point theorem were extended to fuzzy metric spaces. However, the existing extensions require strong additional assumptions. The purpose of this paper is to determine a class of fuzzy metric spaces in which both theorems remain true without the need of any additional condition. We demonstrate the wide validity of the new class.

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 Exact Controllability of an Impulsive Semilinear System with Deviated Argument in a Banach Space

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Sanjukta Das ◽  
Dwijendra N. Pandey ◽  
N. Sukavanam
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Existence And Uniqueness ◽  
Nonlinear Term ◽  
Semigroup Theory ◽  
Exact Controllability ◽  
Impulsive Conditions ◽  
Banach Contraction ◽  
Deviated Argument ◽  
Functional Differential

A functional differential equation with deviated argument coupled with impulsive conditions is studied for the existence and uniqueness of the mild solution and exact controllability of the system. The results are obtained by using Banach contraction principle and C0 semigroup theory without imposing additional assumptions such as analyticity and compactness conditions on the generated semigroup and the nonlinear term. An example is provided to illustrate the presented theory.

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 Study on the Existence of Solutions for a Class of Nonlinear Neutral Hadamard-Type Fractional Integro-Differential Equation with Infinite Delay

2021 ◽  
Vol 5 (2) ◽  
pp. 52
Author(s):  
Kaihong Zhao ◽  
Yue Ma
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Normed Space ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Banach Contraction ◽  
The Banach Contraction Principle

The existence of solutions for a class of nonlinear neutral Hadamard-type fractional integro-differential equations with infinite delay is researched in this paper. By constructing an appropriate normed space and utilizing the Banach contraction principle, Krasnoselskii’s fixed point theorem, we obtain some sufficient conditions for the existence of solutions. Finally, we provide an example to illustrate the validity of our main results.

scholarly journals Optimal Controls for a Class of Impulsive Katugampola Fractional Differential Equations with Nonlocal Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Xingru Chen ◽  
Haibo Gu ◽  
Yu Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Optimal Controls ◽  
Minimizing Sequences ◽  
Fractional Differential

In this paper, we investigate a class of impulsive Katugampola fractional differential equations with nonlocal conditions in a Banach space. First, by using a fixed-point theorem, we obtain the existence results for a class of impulsive Katugampola fractional differential equations. Secondly, we derive the sufficient conditions for optimal controls by building approximating minimizing sequences of functions twice.

scholarly journals New results on Caputo fractional-order neutral differential inclusions without compactness

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Manar A. Alqudah ◽  
C. Ravichandran ◽  
Thabet Abdeljawad ◽  
N. Valliammal
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fractional Order ◽  
Weak Topology ◽  
Differential Inclusions ◽  
Fixed Point Theorems ◽  
Nonlocal Conditions ◽  
Existence Results ◽  
Neutral System

AbstractThis article deals with existence results of Caputo fractional neutral inclusions without compactness in Banach space using weak topology. In fact, for weakly sequentially closed maps we apply fixed point theorems to obtain the existence of the solution. Furthermore, the results are manifested for fractional neutral system held by nonlocal conditions. To justify the application of the reported results an illustration is presented.

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