scholarly journals A discussion concerning the existence results for the Sobolev-type Hilfer fractional delay integro-differential systems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
K. Kavitha ◽  
Kottakkaran Sooppy Nisar ◽  
Anurag Shukla ◽  
Velusamy Vijayakumar ◽  
Shahram Rezapour
Keyword(s):  
Fixed Point ◽  
Nonlocal Condition ◽  
Infinite Delay ◽  
Existence Results ◽  
Sobolev Type ◽  
Differential Systems ◽  
Fractional Delay ◽  
Fractional System ◽  
Fixed Point Technique

AbstractThe goal of this study is to propose the existence results for the Sobolev-type Hilfer fractional integro-differential systems with infinite delay. We intend to implement the outcomes and realities of fractional theory to obtain the main results by Monch’s fixed point technique. Moreover, we show the existence and controllability of the thought about the fractional system with the nonlocal condition. In addition, an application to illustrate the outcomes is also included.

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 Approximate controllability of nonlocal non-autonomous Sobolev type evolution equations

2019 ◽  
Vol 9 (3) ◽  
pp. 86-94
Author(s):  
Arshi Meraj ◽  
Dwijendra Narain Pandey
Keyword(s):  
Fixed Point ◽  
Linear System ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Nonlocal Condition ◽  
Mild Solutions ◽  
Sobolev Type ◽  
Evolution System ◽  
Fixed Point Technique ◽  
Sobolev Type Differential Equations

The aim of this article is to investigate the existence of mild solutions as well as approximate controllability of non-autonomous Sobolev type differential equations with the nonlocal condition. To prove our results, we will take the help of Krasnoselskii fixed point technique, evolution system and controllability of the corresponding linear system.

Approximate controllability for fractional differential equations of sobolev type via properties on resolvent operators

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Yong-Kui Chang ◽  
Aldo Pereira ◽  
Rodrigo Ponce
Keyword(s):  
Fixed Point ◽  
Fractional Derivatives ◽  
Approximate Controllability ◽  
Sobolev Type ◽  
Resolvent Operators ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Norm Continuity ◽  
Fractional Differential ◽  
Fixed Point Technique

AbstractThis paper treats the approximate controllability of fractional differential systems of Sobolev type in Banach spaces. We first characterize the properties on the norm continuity and compactness of some resolvent operators (also called solution operators). And then via the obtained properties on resolvent operators and fixed point technique, we give some approximate controllability results for Sobolev type fractional differential systems in the Caputo and Riemann-Liouville fractional derivatives with order 1 <

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.   

scholarly journals Controllability of Fractional Neutral Stochastic Integro-Differential Systems with Infinite Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xichao Sun ◽  
Litan Yan ◽  
Jing Cui
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Abstract Space ◽  
Differential Systems ◽  
Compactness Condition ◽  
Fixed Point Principle ◽  
Controllability Result

This paper is concerned with the controllability of a class of fractional neutral stochastic integro-differential systems with infinite delay in an abstract space. By employing fractional calculus and Sadovskii's fixed point principle without assuming severe compactness condition on the semigroup, a set of sufficient conditions are derived for achieving the controllability result.

scholarly journals Existence results of solutions for some fractional neutral functional integro-differential equations with infinite delay

2017 ◽  
Author(s):  
Kazem Nouri ◽  
Marjan Nazari ◽  
Bagher Keramati
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Infinite Delay ◽  
Existence Results ◽  
Banach Fixed Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fractional Equations

In this paper, by means of the Banach fixed point theorem and the Krasnoselskii's fixed point theorem, we investigate the existence of solutions for some fractional neutral functional integro-differential equations involving infinite delay. This paper deals with the fractional equations in the sense of Caputo fractional derivative and in the Banach spaces. Our results generalize the previous works on this issue. Also, an analytical example is presented to illustrate our results.

scholarly journals Approximate Controllability of Fractional Neutral Evolution Equations in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. I. Mahmudov
Keyword(s):  
Fixed Point ◽  
Approximate Controllability ◽  
Evolution Equations ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Neutral Evolution ◽  
Differential Systems ◽  
Neutral Differential Equations ◽  
Approximately Controllable ◽  
Fractional Neutral Evolution Equations

We discuss the approximate controllability of semilinear fractional neutral differential systems with infinite delay under the assumptions that the corresponding linear system is approximately controllable. Using Krasnoselkii's fixed-point theorem, fractional calculus, and methods of controllability theory, a new set of sufficient conditions for approximate controllability of fractional neutral differential equations with infinite delay are formulated and proved. The results of the paper are generalization and continuation of the recent results on this issue.

scholarly journals New existence results for solutions of BVPs for higher order IFDEs involving Riemann-Liouville type Hadamard fractional derivatives

Filomat ◽  
2018 ◽  
Vol 32 (11) ◽  
pp. 3957-3991
Author(s):  
Yuji Liu ◽  
Xiaohui Yang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Fractional Derivatives ◽  
Boundary Value ◽  
Existence Results ◽  
Liouville Type ◽  
Differential Systems ◽  
Fractional Differential Systems ◽  
Integral Systems ◽  
Fractional Differential

In this article, we present a method for converting boundary value problems for impulsive fractional differential systems involving the Riemann-Liouville type Hadamard fractional derivatives to integral systems. The existence results for solutions of this kind of boundary value problems are established. Our analysis relies on the well known fixed point theorem. Some comments on recent published papers are made at the end of the paper.

scholarly journals EXISTENCE RESULTS FOR NEUTRAL IMPULSIVE QUASILINEAR MIXED VOLTERRA-FREDHOLM TYPE INTEGRODIFFERENTIAL SYSTEMS

2020 ◽  
pp. 83-92
Author(s):  
NARESH KUMAR JOTHI ◽  
K. A. VENKATESAN ◽  
T. GUNASEKAR ◽  
F. PAUL SAMUEL
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Fredholm Type ◽  
Impulsive Conditions ◽  
Fixed Point Technique

The paper deals with the study of existence of solutions for quasilinear neutral mixed Volterra-Fredholm-type integrodifferential equations with nonlocal and impulsive conditions in Banach spaces. The results are obtained by using a fixed point technique and semigroup theory

EXISTENCE AND CONTROLLABILITY RESULTS FOR INFINITE DELAY PARTIAL FUNCTIONAL DIFFERENTIAL SYSTEMS WITH MULTI-VALUED IMPULSES IN BANACH SPACES

2010 ◽  
Vol 03 (04) ◽  
pp. 631-646 ◽  
Author(s):  
Hanwen Ning ◽  
Bing Liu
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Differential Systems ◽  
Functional Differential Systems ◽  
Functional Differential

This paper is concerned with the existence and controllability of solutions for infinite delay functional differential systems with multi-valued impulses in Banach space. Sufficient conditions for the existence are obtained by using a fixed point theorem for multi-valued maps due to Dhage. An example is also given to illustrate our results.

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