Integro-differential Inclusions Research Articles

Optimal Solutions for a Class of Impulsive Differential Problems with Feedback Controls and Volterra-Type Distributed Delay: A Topological Approach

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established for when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is reformulated within the class of impulsive semilinear integro-differential inclusions in Banach spaces and is studied by using topological methods and multivalued analysis. The paper concludes with an application to a population dynamics model.

EXISTENCE AND CONTINUOUS DEPENDENCE RESULTS FOR VOLTERRA-FREDHOLM INCLUSION

The solvability of a state-dependent integro-differential inclusion is the main focus of this research. A state-dependent Volterra-Fredholm integro-differential inclusion (V-FIDI) with a nonlocal condition is explored, along with the existence and uniqueness of its solutions. We first prove the existence and uniqueness properties of the solution under certain assumptions about the given data. Lastly, a sample that highlights the primary finding is provided.

On controllability for Sobolev-type fuzzy Hilfer fractional integro-differential inclusions with Clarke subdifferential

In this paper, our main purpose is to search and obtain the controllability for Sobolev-type fuzzy Hilfer fractional integro-differential inclusions with Clarke subdifferential. Some sufficient conditions for the controllability results of this inclusion problem are proposed by using related techniques of fuzzy set theory, Sobolev-type, fractional calculus and Clarke subdifferential. The theorem of the controllability results is proved by Bohnenblust–Karlin fixed point theorem. In addition, we show an example to explain the controllability results of this inclusion problem.

Solution Sets for Second-Order Integro-Differential Inclusions with Infinite Delay

Solution Sets for Second-Order Integro-Differential Inclusions with Infinite Delay

Generalized Almost Periodicity in Measure

This paper investigates diverse classes of multidimensional Weyl and Doss ρ-almost periodic functions in a general measure setting. This study establishes the fundamental structural properties of these generalized ρ-almost periodic functions, extending previous classes such as m-almost periodic and (equi-)Weyl-p-almost periodic functions. Notably, a new class of (equi-)Weyl-p-almost periodic functions is introduced, where the exponent p>0 is general. This paper delves into the abstract Volterra integro-differential inclusions, showcasing the practical implications of the derived results. This work builds upon the extensions made in the realm of Levitan N-almost periodic functions, contributing to the broader understanding of mathematical functions in diverse measure spaces.

A study of nonlocal fractional neutral stochastic integrodifferential inclusions of order 1

This paper considers a class of nonlocal fractional neutral stochastic integrodifferential inclusions of order 1 < α < 2 with impulses in a Hilbert space. We study the existence of the mild solution for the cases when the multi-valued map has convex and non-convex values. The results are obtained by combining fixed-point theorems with the fractional order cosine family, semigroup theory, and stochastic techniques. A new set of sufficient conditions is developed to demonstrate the approximate controllability of the system. Finally, an example is given to illustrate the obtained results.

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutral‐type fractional stochastic integrodifferential inclusions with infinite delay and non‐instantaneous impulse in a separable Hilbert space using the Atangana–Baleanu Caputo fractional derivative. We investigate the existence of a mild solution for the Atangana–Baleanu Caputo fractional neutral‐type delay integrodifferential stochastic system while taking into account the non‐instantaneous impulses. For this purpose, the Atangana–Baleanu Caputo fractional neutral‐type impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the Bohnenblust–Karlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper.

Existence Results of Random Impulsive Integrodifferential Inclusions with Time-Varying Delays

This study examines the existence of mild solutions for nonlinear random impulsive integrodifferential inclusions with time-varying delays under sufficient conditions. Our study is based on the Martelli fixed point theorem, Pachpatte’s inequality, and the fixed point theorem due to Covitz and Nadler. Besides, we generalize, extend, and develop some well-known results in the existing literature.

Solving delay integro-differential inclusions with applications

&lt;abstract&gt;&lt;p&gt;This work primarily delves into three key areas: the presence of mild solutions, exploration of the topological and geometrical makeup of solution sets, and the continuous dependency of solutions on a second-order semilinear integro-differential inclusion. The Bohnenblust-Karlin fixed-point method has been integrated with Grimmer's theory of resolvent operators. Ultimately, the study delves into a mild solution for a partial integro-differential inclusion to showcase the achieved outcomes.&lt;/p&gt;&lt;/abstract&gt;

Approximate controllability for some retarded integrodifferential inclusions using a version of the Leray-Schauder fixed point theorem for the multivalued maps

Approximate controllability for some retarded integrodifferential inclusions using a version of the Leray-Schauder fixed point theorem for the multivalued maps

Existence Results on Mittag-Leffler Kernel of Fractional Integro-Differential Inclusion Problem Under Boundary Conditions

Existence Results on Mittag-Leffler Kernel of Fractional Integro-Differential Inclusion Problem Under Boundary Conditions

Weak solutions of a fractional orders quadratic functional integro-differential inclusion in a reflexive Banach space

Weak solutions of a fractional orders quadratic functional integro-differential inclusion in a reflexive Banach space

On a Hilfer type fractional integro-differential inclusion

A boundary value problem associated to a Hilfer generalized proportional fractional integro-differential inclusion is studied. The existence of solutions is established in the case when the set-valued map has nonconvex values.

Further investigation of stochastic nonlinear Hilfer-fractional integro-differential inclusions using almost sectorial operators

Further investigation of stochastic nonlinear Hilfer-fractional integro-differential inclusions using almost sectorial operators

Sobolev‐type existence results for impulsive nonlocal fractional stochastic integrodifferential inclusions of order ϱ∈(1,2) with infinite delay via sectorial operator

The impulsive effect on the fractional stochastic integrodifferential system of order with infinite delay via sectorial operator is investigated in this work. The primary findings of this study are tested by referring to multivalued functions, sectorial operators, fractional derivatives, and the fixed point approach. Initially, the presence of a mild solution for the systems class was introduced. The existence outcomes of semilinear control problems were then established. Eventually, an application is given for deriving the theory of the key findings.

Asymptotically almost periodic mild solutions for some partial integrodifferential inclusions using scale of Banach spaces

Abstract We are interested in the existence of mild solutions for a class of partial integrodifferential inclusions in infinite dimensional Banach spaces. First, we show the existence of mild solutions with the help of a scale of Banach spaces, the theory of resolvent operators, and the fixed point theory for the measure of non-compactness. Moreover, we examine the existence of asymptotically almost periodic solutions for our problem. Finally, an example of the abstract results is provided.

An analysis on the approximate controllability of neutral impulsive stochastic integrodifferential inclusions via resolvent operators

This article focuses on the approximate controllability of impulsive neutral stochastic integrodifferential inclusions in Hilbert spaces. We used resolvent operators, fixed point approaches, and semigroup theory to achieve the article's main results. First, we focus on the existence of approximate controllability, and we develop the existence results with nonlocal conditions. At last, an application is provided to illustrate the concept.

Existence trajectory and optimal control of Clarke subdifferential stochastic integrodifferential inclusions suffered by non-instantaneous impulses and deviated arguments

In this article, the solvability, Trajectory(T-) and optimal controllability of stochastic integrodifferential inclusions with Clarke subdifferential along with deviated arguments and Poisson jumps are analyzed which are new and untreated topics in the literature. The theory of resolvent operators, stochastic analysis, semigroup theory and a multivalued fixed point theorem are used to prove the solvability of the proposed non-instantaneous impulsive stochastic integrodifferential inclusion in Hilbert space. In addition, the strongest notion of controllability called T-controllability of the system is determined using a generalized Gronwall inequality with some appropriate assumptions. Following that, we derive the existence of optimal control of the proposed problem using Balder’s theorem. A numerical example is given to validate the theoretical aspects. We study the numerical simulation of the proposed problem with challenges. An abstract application of a stochastic dam contamination model is studied to justify the developed theoretical result. This paper contains the study of T-control along with the optimal control. This work is the unique combination of theoretical and numerical simulation as well as the real life application.

On S-asymptotically $$\omega$$-periodic mild solutions of some integrodifferential inclusions of Volterra-type

On S-asymptotically $$\omega$$-periodic mild solutions of some integrodifferential inclusions of Volterra-type

A study on the approximate controllability results of fractional stochastic integro-differential inclusion systems via sectorial operators

The study deals with the findings of the outcome of the approximate controllability results of inclusion type fractional stochastic system in Banach space with the order of the fractional system varrho in (1,2). At first, we implement Bohnenblust-Karlin's fixed point technique to deduce the required conditions on which the fractional system with inital conditions is approximately controllable, and there by, we postulate the sufficient conditions for extending the obtained results to the system with nonlocal conditions.