Differential Inclusions Of Fractional Order Research Articles

Existence of Solutions of Impulsive Partial Hyperbolic Differential Inclusion of Fractional Order

This paper is concerned with the existence of solutions of a class of Cauchy problems for hyperbolic partial fractional differential inclusions (HPFD) involving the Caputo fractional derivative with an impulse whose right hand side is convex and non-convex valued. Our results are achieved within the framework of the nonlinear alternative of Leray-Schauder type and contraction multivalued maps. A detailed example was provided to support the theorem.

Darboux problem for fractional partial hyperbolic di erential inclusions on unbounded domains with delay

"In this paper we investigate the existence of solutions of initial value problems (IVP for short), for partial hyperbolic functional and neutral differential inclusions of fractional order involving Caputo fractional derivative with finite delay by using the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces."

О существовании решения периодической краевой задачи для полулинейных дифференциальных включений дробного порядка в банаховых пространствах

In this paper, we study a periodic boundary value problem for a class of semilinear differential inclusions of fractional order in a Banach space for which the multivalued nonlinearity satisfies the regularity condition expressed in terms of measures of noncompactness. To prove the existence of solutions to the problem, we first construct the corresponding Green function. Then we introduce into consideration a multivalued resolving operator in the space of continuous functions and reduce the posed problem to the existence of fixed points of the resolving multioperator. To prove the existence of a fixed point, a generalized theorem of B.N. Sadovskii type for a condensing multivalued map is used.

Fractional order differential inclusions on an unbounded domain with infinite delay

We provide sufficient conditions for the existence of solutions to initial value problems, for partial hyperbolic differential inclusions of fractional order involving Caputo fractional derivative with infinite delay by applying the nonlinear alternative of Frigon type for multivalued admissible contraction in Frechet spaces.

On the Boundary Value Problem for Functional Differential Inclusion of Fractional Order with General Initial Condition in a Banach Space

We consider the problem for a functional differential inclusion of fractional order with a general initial condition expressed in the form of an operator inclusion in a Banach space. At the beginning of the paper, an introduction is presented in which the relevance of the study is substantiated, then preliminary information from fractional analysis, the theory of measures of noncompactness and condensing mappings, as well as some information from multivalued analysis are given. In the second subsection, we state the problem and its solution on the basis of the theory of condensing multivalued mappings. In the last subsection, we give an example of a particular case of the solved problem, in the case of an antiperiodic boundary condition.

О краевой задаче для фунционально-дифференциального включения дробного порядка с общим начальным условием в банаховом пространстве

О краевой задаче для фунционально-дифференциального включения дробного порядка с общим начальным условием в банаховом пространстве

АППРОКСИМАЦИЯ ГИПЕРБОЛИЧЕСКИХ ДИФФЕРЕНЦИАЛЬНЫХ ВКЛЮЧЕНИЙ ДРОБНОГО ПОРЯДКА С ИМПУЛЬСНЫМИ ВОЗДЕЙСТВИЯМИ

In this paper there are considered hyperbolic differential inclusions of fractional order with impulses. Here we represent the concept of approximate solution (δ-solution) for a hyperbolic differential inclusion of fractional order with impulses. The asymptotic properties of solutions sets to approximating differential inclusions of fractional order with external disturbance are derived.

On semidiscretization methods for differential inclusions of fractional order

On semidiscretization methods for differential inclusions of fractional order

О задаче Коши для функционально-дифференциального включения дробного порядка с общим начальным условием в банаховом пространстве

О задаче Коши для функционально-дифференциального включения дробного порядка с общим начальным условием в банаховом пространстве

ОБ ОДНОЙ ЗАДАЧЕ УПРАВЛЯЕМОСТИ ДЛЯ ДИФФЕРЕНЦИАЛЬНОГО ВКЛЮЧЕНИЯ С ДРОБНОЙ ПРОИЗВОДНОЙ КАПУТО

The paper gives the controllability problem for a differential inclusion of fractional order in a Banach space.

Boundary value problems for semilinear differential inclusions of fractional order in a Banach space

In the present paper, we show that the solution set of a fractional order semilinear differential inclusion in a Banach space has the topological structure of an -set. This result allows to apply a fixed point result for condensing multimaps to the translation multioperator along the trajectories of such inclusion and to prove the existence of solutions satisfying periodic and anti-periodic boundary value conditions. An example concerning with a fractional order feedback control system is presented.

On a Sturm-Liouville type differential inclusion of fractional order

On a Sturm-Liouville type differential inclusion of fractional order

On Existence of Fractional Integral and Anti-Periodic Boundary Valued Problem for Differential Inclusion of Fractional Order α ∈ (4, 5

On Existence of Fractional Integral and Anti-Periodic Boundary Valued Problem for Differential Inclusion of Fractional Order <i>α</i> ∈ (4, 5

Impulsive functional delay differential inclusions of fractional order at variable times

We are concerned with some sufficient conditions for the existence of solutions of a class of initial value problems for impulsive fractional differential inclusions with functional delay at variable moments.

Об индексе множества решений задачи Коши для дифференциального включения дробного порядка в банаховом пространстве

Об индексе множества решений задачи Коши для дифференциального включения дробного порядка в банаховом пространстве

Об уплотняущем мультиотображении для дифференциального включения дробного порядка

Об уплотняущем мультиотображении для дифференциального включения дробного порядка

О задаче Коши для одного класса дифференциальных включений дробного порядка с почти полунепрерывной снизу правой частью

О задаче Коши для одного класса дифференциальных включений дробного порядка с почти полунепрерывной снизу правой частью

О задаче Коши для дифференциального включения дробного порядка в банаховом пространстве

О задаче Коши для дифференциального включения дробного порядка в банаховом пространстве

Some existence results for differential inclusions of fractional order with nonlocal strip conditions

In this paper, the existence of solutions for differential inclusions of fractional order with nonlocal strip conditions is investigated. Our study includes two cases: (i) the multivalued map involved in the problem is not necessarily convex valued, (ii) the multivalued map consists of non-convex values. We combine the nonlinear alternative of Leray-Schauder type coupled with the selection theorem of Bressan and Colombo to establish the first result, while the second result relies on Wegrzyk’s fixed point theorem for generalized contractions. MSC:34A08, 34B10, 34B15.

Positive Solutions of Fractional Differential Inclusions at Resonance

This paper deals with the fractional differential inclusions at resonance. By the recent Leggett-Williams theorem for coincidences of multi-valued operators due to O’Regan and Zima in [19], we present a new result on the existence of positive solutions for a class of differential inclusion of fractional order with boundary conditions at resonance. And our results improve and generalize the existing results.