Integro-differential Inclusions Research Articles

Time-varying integro-differential inclusions with Clarke sub-differential and non-local initial conditions: existence and approximate controllability

In this paper, we mainly consider a time-varying semi-linear integro-differential inclusion with Clarke sub-differential and a non-local initial condition. By a suitable Green function combined with a resolvent operator, we firstly formulate its mild solutions and show that it admits at least one mild solution which can exist in a well-defined ball with a radius big enough. Through constructing a proper functional, we then derive a useful characterization of the approximate controllability for its related linear system in Green function terms, and establish a sufficient condition for the approximate controllability of the time-varying semi-linear integro-differential inclusion. Lastly, we also consider the finite approximate controllability of the time-varying semi-linear integro-differential inclusion via variational method.

Approximate controllability of Hilfer fractional Sobolev type integrodifferential inclusions with nonlocal conditions

Approximate controllability of Hilfer fractional Sobolev type integrodifferential inclusions with nonlocal conditions

Approximate controllability of Hilfer fractional Sobolev type integrodifferential inclusions with nonlocal conditions

In this paper, we investigate approximate controllability of Hilfer fractional Sobolev type differential inclusions with nonlocal conditions. The main techniques rely on the fixed point theorem combined with the semigroup theory, fractional calculus and multivalued analysis. An example is provided to illustrate the obtained results.

On nonlinear mixed fractional integrodifferential inclusion with four-point nonlocal Riemann-Liouville integral boundary conditions

The aim of the present paper is to establish the existence of solutions of nonlinear mixed fractional integrodifferential inclusion with four-point nonlocal Riemann-Liouville integral boundary conditions in Banach spaces.

Approximate Controllability of Second-order Neutral Stochastic Non-autonomous Integrodifferential Inclusionsby Resolvent Operators

In this paper, we formulate a set of sufficient conditions for the approximate controllability for a class of second-order neutral stochastic nonautonomous integrodifferential inclusions in Hilbert space. We establish the results with the help of resolvent operators and Bohnenblust-Karlin’s fixed point theorem is to prove the main result. An application is given to illustrate the main result.

Some qualitative properties of mild solutions of a second-order integro-differential inclusion

We prove the Lipschitz dependence on the initial data of the solution set of a Cauchy problem associated to a second-order integro-differential inclusion by using the contraction principle in the space of selections of the multifunction instead of the space of solutions. A Filippov type existence theorem for this problem is also provided.

On fractional integro-differential inclusions via the extended fractional Caputo\u2013Fabrizio derivation

We first show that four fractional integro-differential inclusions have solutions. Also, we show that dimension of the set of solutions for the second fractional integro-differential inclusion problem is infinite dimensional under some different conditions.

On dimension of the set of solutions of a fractional differential inclusion via the Caputo-Hadamard fractional derivation

We investigate the existence of solution for a fractional integro-differential inclusion via the Caputo-Hadamard fractional derivation. We prove that dimension of the set of solutions for the inclusion problem isinfinite dimensional under some conditions.

Averaging Scheme for Integrodifferential Inclusions

We substantiate an averaging scheme for integrodifferential inclusions on a bounded interval.

Results on approximate controllability of second-order non-autonomous integrodifferential inclusions via resolvent operators

In this work, we establish a set of sufficient conditions for the approximate controllability for a class of non-autonomous second-order integrodifferential inclusions in Banach spaces. We establish our main results with the help of resolvent operators and Bohnenblust-Karlin's fixed point theorem. Then we extend our study to second-order neutral systems with nonlocal conditions. An example is given to illustrate the main result.

Results on approximate controllability of second-order non-autonomous integrodifferential inclusions via resolvent operators

Results on approximate controllability of second-order non-autonomous integrodifferential inclusions via resolvent operators

On the Solutions of a Class of Fractional Hyperbolic Integro-Differential Inclusions

We study a Darboux problem associated to a fractional hyperbolic integro-differential inclusion defined by Caputo-Katugampola fractional derivative and we prove several existence results for this problem.

On some fractional integro-differential inclusions with nonlocal multi-point boundary conditions

On some fractional integro-differential inclusions with nonlocal multi-point boundary conditions

Continuous Family of Solutions for Fractional Integro-Differential Inclusions of Caputo-Katugampola Type

Continuous Family of Solutions for Fractional Integro-Differential Inclusions of Caputo-Katugampola Type

О разрешимости каузальных функциональных включений с бесконечным запаздыванием

In the present article we develop the results of works devoted to the study of problems for functional differential equations and inclusions with causal operators, in case of infinite delay. In the introduction of the article we substantiates the relevance of the research topic and provides links to relevant works A. N. Tikhonov, C. Corduneanu, A. I. Bulgakov, E. S. Zhukovskii, V. V. Obukhovskii and P. Zecca. In section two we present the necessary information from the theory of condensing multivalued maps and measures of noncompactness, also introduced the concept of a multivalued causal operator with infinite delay and illustrated it by examples. In the next section we formulate the Cauchy problem for functional inclusion, containing the composition of multivalued and single-valued causal operators; we study the properties of the multiopera-tor whose fixed points are solutions of the problem. In particular, sufficient conditions under which this multioperator is condensing on the respective measures of noncompacness. On this basis, in section four we prove local and global results and continuous dependence of the solution set on initial data. Next the case of inclusions with lower semicontinuous causal multioperators is considered. In the last section we generalize some results for semilinear differential inclusions and Volterra integrodifferential inclusions with infinite delay.

On the mild solutions of a class of second-order integro-differential inclusions

On the mild solutions of a class of second-order integro-differential inclusions

The controllability of an impulsive integro-differential process with nonlocal feedback controls

The controllability of an impulsive process governed by a parametric integro-differential equation involving a Volterra operator is shown. The model is studied via the existence of impulsive mild solutions for a semilinear integro-differential inclusion. A discussion on the impulse functions is presented.

Approximate controllability of neutral integrodifferential inclusions via resolvent operators

In this work, a set of sufficient conditions are established for the approximate controllability for neutral integrodifferential inclusions in Banach spaces. The theory of fractional power and α-norm is used because of the spatial derivatives in the nonlinear term of the system. Bohnenblust-Karlin's fixed point theorem is used to prove our main results. Further, this result is extended to study the approximate controllability for nonlinear functional control system with nonlocal conditions. An example is also given to illustrate our main results.

Approximate controllability of second-order stochastic non-autonomous integrodifferential inclusions by resolvent operators

In this paper, we formulate a set of sufficient conditions for the approximate controllability for a class of second-order stochastic non-autonomous integrodifferential inclusions in Hilbert space. We establish the results with the help of resolvent operators and Bohnenblust-Karlin's fixed point theorem is to prove the main result. An application is given to illustrate the main result.

Existence of a mild solution for a neutral stochastic fractional integro-differential inclusion with a nonlocal condition

This paper mainly concerns the existence of a mild solution for a neutral stochastic fractional integro-differential inclusion of order $1\lt \beta \lt 2$ with a nonlocal con\-dition in a separable Hilbert space. Utilizing the fixed point theorem for multi-valued operators due to O' Regan, we establish an existence result involving a $\beta $-resolvent operator. An illustrative example is provided to show the effectiveness of the established results.