scholarly journals Holder's Inequality ρ–Mean Continuity for Existence and Uniqueness Solution of Fractional Multi-Integrodifferential Delay System

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Sameer Qasim Hasan
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlocal Condition ◽  
Infinite Delay ◽  
Hölder’S Inequality ◽  
Sufficient Conditions ◽  
Delay System ◽  
Linear Operators ◽  
Bounded Linear ◽  
Hölder's Inequality

We herein present the detailed results for the existence and uniqueness of mild solution for multifractional order impulsive integrodifferential control equations with a nonlocal condition involving several types of semigroups of bounded linear operators, which were established on probability density functions related with the fractional differential equation. Additionally, we present the necessary and sufficient conditions to investigate Schauder’s fixed point theorem with Holder’s inequality ρ–mean continuity and infinite delay parameter to guarantee the uniqueness of a fixed point.

scholarly journals Existence of Second Order Impulsive Neutral Integro-Differential Evolution Control Systems with an Infinite Delay

2019 ◽  
Vol 8 (3) ◽  
pp. 8857-8862
Keyword(s):  
Fixed Point ◽  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Cosine Families ◽  
Evolution Control ◽  
Evolution Systems

This article, we study sufficient conditions for the controllability of second-order impulsive neutral integrodifferential evolution systems with an infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

scholarly journals On Approximate Controllability of Second-Order Neutral Partial Stochastic Functional Integrodifferential Inclusions with Infinite Delay and Impulsive Effects

2015 ◽  
Vol 2015 ◽  
pp. 1-26 ◽  
Author(s):  
Zuomao Yan
Keyword(s):  
Stochastic Analysis ◽  
Approximate Controllability ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Bounded Linear ◽  
Approximation Techniques ◽  
Approximately Controllable ◽  
Stochastic Functional

We discuss the approximate controllability of second-order impulsive neutral partial stochastic functional integrodifferential inclusions with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using the fixed point strategy, stochastic analysis, and properties of the cosine family of bounded linear operators combined with approximation techniques, a new set of sufficient conditions for approximate controllability of the second-order impulsive partial stochastic integrodifferential systems are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.

scholarly journals A Study of Second Order Impulsive Neutral Evolution Differential Control Systems with an Infinite Delay

2018 ◽  
Author(s):  
P. Palani ◽  
T. Gunasekar ◽  
M. Angayarkanni ◽  
D. Kesavan
Keyword(s):  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Neutral Evolution ◽  
Differential Systems ◽  
Bounded Linear ◽  
Cosine Families ◽  
Differential Control

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

scholarly journals Observability of Fractional-Order Impulsive Control Integro-Differential System with Nonlocal Initial Condition

2020 ◽  
Vol 55 (1) ◽  
Author(s):  
Sameer Qasim Hasan
Keyword(s):  
Fixed Point ◽  
Fractional Order ◽  
Differential System ◽  
Impulsive Control ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Linear Operators ◽  
Necessary Condition ◽  
Primary Role ◽  
Bounded Linear

The article describes a new concept for initial and exactly observability of nonlocal fractional-order impulsive control integro-differential system. This is based on the concepts of the abstract Cauchy problem, which depended on some necessary and sufficient conditions. These conditions established on the semigroup theory of bounded operators as a dynamical operator system, which generated by bounded linear operators. Moreover, invertible operators play a primary role, and we presented a necessary condition for some nonlinear multi variables functions. Thus, all these operators were treated in nonlinear functional analysis to guaranty the initial observable and exactly observability. Therefore, from the mild solution of the system and exactly homogenous part, we proved the equivalent concepts between the initial observability and exactly the observability. Thus, our approach in this article is to prove the uniqueness of initial nonlocal values with admissible control, which belongs to the second-order Lebesgue integrable. The interest of observability results in this article lies by proving a unique fixed point, which is nonlocal initial values that are described in the proposal formula by using Banach’s fixed point theory. The processing observability for complexly systems (such as this system) with all components and properties was established and can be used for many control system applications.

scholarly journals A Study of Second Order Impulsive Neutral Evolution Control Systems with an Infinite Delay

2018 ◽  
Author(s):  
Perumal Palani ◽  
Tharmalingam Gunasekar ◽  
M. Angayarkanni ◽  
D. Kesavan
Keyword(s):  
Control Systems ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Operators ◽  
Neutral Evolution ◽  
Bounded Linear ◽  
Cosine Families ◽  
Evolution Control ◽  
Evolution Systems

This article, we study sufficient conditions for the controllability of second-order impulsive partial neutral evolution systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

Controllability for some nonlinear impulsive partial functional integrodifferential systems with infinite delay in Banach spaces

2020 ◽  
Vol 4 (2) ◽  
pp. 104-115
Author(s):  
Khalil Ezzinbi ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Resolvent Operator ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Mönch Fixed Point Theorem ◽  
The Resolvent Operator

This work concerns the study of the controllability for some impulsive partial functional integrodifferential equation with infinite delay in Banach spaces. We give sufficient conditions that ensure the controllability of the system by supposing that its undelayed part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point Theorem. As a result, we obtain a generalization of the work of K. Balachandran and R. Sakthivel (Journal of Mathematical Analysis and Applications, 255, 447-457, (2001)) and a host of important results in the literature, without assuming the compactness of the resolvent operator. An example is given for illustration.

scholarly journals Existence and Uniqueness of Solutions to the Wage Equation of Dixit-Stiglitz-Krugman Model with No Restriction on Transport Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Minoru Tabata ◽  
Nobuoki Eshima
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Nonlinear Operator ◽  
Sufficient Conditions ◽  
Wage Equation ◽  
Discrete Equation ◽  
Transport Costs ◽  
Economic Activities ◽  
Uniqueness Of Solutions ◽  
Double Nonlinear

In spatial economics, the distribution of wages is described by a solution to the wage equation of Dixit-Stiglitz-Krugman model. The wage equation is a discrete equation that has a double nonlinear singular structure in the sense that the equation contains a discrete nonlinear operator whose kernel itself is expressed by another discrete nonlinear operator with a singularity. In this article, no restrictions are imposed on the maximum of transport costs of the model and on the number of regions where economic activities are conducted. Applying Brouwer fixed point theorem to this discrete double nonlinear singular operator, we prove sufficient conditions for the wage equation to have a solution and a unique one.

scholarly journals Existence and Uniqueness of Solutions to Third-Order Boundary Value Problems

2021 ◽  
Vol 22 (2) ◽  
pp. 221-240
Author(s):  
S. S. Almuthaybiri ◽  
J. M. Jonnalagadda ◽  
C. C. Tisdell
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Third Order ◽  
Fixed Point Methods ◽  
Bounded Sets

The purpose of this research is to connect fixed point methods with certain third-order boundary value problems in new and interesting ways. Our strategy involves an analysis of the problem under consideration within closed and bounded sets. We develop sufficient conditions under which the associated mappings will be contractive and invariant in these sets, which generates new advances concerning the existence, uniqueness and approximation of solutions.

scholarly journals Common Fixed-Point Results in Ordered Left (Right) Quasi- b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Hemant Kumar Nashine ◽  
Sourav Shil ◽  
Hiranmoy Garai ◽  
Lakshmi Kanta Dey ◽  
Vahid Parvaneh
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Ordered Sets ◽  
Nonlinear Matrix ◽  
Fractional Differential ◽  
Left And Right

We use the notions of left- and right-complete quasi- b -metric spaces and partial ordered sets to obtain a couple of common fixed-point results for strictly weakly isotone increasing mappings and relatively weakly increasing mappings, which satisfy a pair of almost generalized contractive conditions. To illustrate our results, throughout the paper, we give several relevant examples. Further, we use our results to establish sufficient conditions for existence and uniqueness of solution of a system of nonlinear matrix equations and a pair of fractional differential equations. Finally, we provide a nontrivial example to validate the sufficient conditions for nonlinear matrix equations with numerical approximations.

scholarly journals The Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Differential Equations with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Azizollah Babakhani ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Infinite Delay ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Fractional Differential

We prove the existence and uniqueness of solutions for two classes of infinite delay nonlinear fractional order differential equations involving Riemann-Liouville fractional derivatives. The analysis is based on the alternative of the Leray-Schauder fixed-point theorem, the Banach fixed-point theorem, and the Arzela-Ascoli theorem inΩ={y:(−∞,b]→ℝ:y|(−∞,0]∈ℬ}such thaty|[0,b]is continuous andℬis a phase space.

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