ANTI-PERIODIC SOLUTIONS FOR DIFFERENTIAL INCLUSIONS IN BANACH SPACES AND THEIR APPLICATIONS

We deal with anti-periodic problems for differential inclusions with nonmonotone perturbations. The main tools in our study are the maximal monotone property of the derivative operator with anti-periodic conditions and the theory of pseudomonotone perturbations of maximal monotone mappings. We then apply our results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.

Controllability of Fractional Order Stochastic Differential Inclusions with Fractional Brownian Motion in Finite Dimensional Space

In this paper,sufficient conditions are formulated for controllability of fractional order stochastic differential inclusions with fractional Brownian motion(f Bm) via fixed point theorems,namely the Bohnenblust-Karlin fixed point theorem for the convex case and the Covitz-Nadler fixed point theorem for the nonconvex case.The controllability Grammian matrix is defined by using Mittag-Leffler matrix function.Finally,a numerical example is presented to illustrate the efficiency of the obtained theoretical results.

CONTINUOUS SELECTIONS OF SOLUTION SETS OF FRACTIONAL INTEGRO-DIFFERENTIAL INCLUSIONS

Using Bressan-Colombo results, concerning the existence of continuous selections of lower semicontinuous multifunctions with decomposable values, we prove a continuous version of Filippov＇s theorem for a fractional integro-differential inclusion involving Caputo＇s fractional derivative. This result allows us to obtain a continuous selection of the solution set of the problem considered.

Existence of solutions for implicit fuzzy differential inclusions

A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions （FDIs） and fuzzy differential equations （FDEs）, which might be helpful in the analysis of fuzzy dynamic systems.

ON THE PERIODIC SOLUTIONS OF DIFFERENTIAL INCLUSIONS AND APPLICATIONS

The periodic problem of evolution inclusion is studied and its results are used to establish existence theorems of periodic solutions of a class of semi_linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given for this class of semi_linear differential inclusion. An application to some feedback control systems is discussed.

EXISTENCE OF SOLUTIONS FORP ARABOLIC TYPE EVOLUTION DIFFERENTIAL INCLUSIONS AND THE PROPERTY OF THE SOLUTION SET

In this paper, parabolic type differential inclusions with time dependent ape considered and this problem is related to the study of the nonlinear distributed parameter central systems. An existence theorem of mild-solutions is proved, and a property of the solution set is given. The directions and the results by J.P. Aubin et al. are generalized and improved.

Existence of Periodic Solutions for Differential Inclusions

This paper deals with the periodic solution theory to differential inclusions related to periodic optimal control problems. The results of Halanay and Yoshizawa are presented for multivalued systems.

Lyapunov stability and generalized invariance principle for nonconvex differential inclusions

This paper studies the system stability problems of a class of nonconvex differential inclusions. At first, a basic stability result is obtained by virtue of locally Lipschitz continuous Lyapunov functions. Moreover, a generalized invariance principle and related attraction conditions are proposed and proved to overcome the technical difficulties due to the absence of convexity. In the technical analysis, a novel set-valued derivative is proposed to deal with nonsmooth systems and nonsmooth Lyapunov functions. Additionally, the obtained results are consistent with the existing ones in the case of convex differential inclusions with regular Lyapunov functions. Finally, illustrative examples are given to show the effectiveness of the methods.

Impulsive Boundary Value Problems for First-order Ordinary Differential Inclusions

In this paper, we investigate the existence of solutions for impulsive first order ordinary differential inclusions which admitting nonconvex valued right hand side. We present two classes of results. In the first one, we rely on a fixed point theorem for contraction multivalued maps due to Covitz and Nadler, and for the second one, we use Schacfer＇s fixed point theorem combined with lower semi-continuous multivalued operators with decomposable values under weaker conditions.

Uncertainty in public health models treated by differential inclusions

An application of differential inclusions in the epidemic spread models is presented.Some mostly used epidemic models are discussed here,and a brief survey of epidemic modeling is given.Most of the models are some modifications of the Susceptible–Infected–Recovered model.Simple simulations are carried out.Then,we consider the influence of some uncertain parameters.It is pointed out that the presence of some fluctuating model parameters can be treated by differential inclusions.The solution to such differential inclusion is given in the form of reachable sets for model variables.Here,we focus on the differential inclusion application rather than the model construction.

On Systems of Boundary Value Problems for Differential Inclusions

Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.

NONDENSELY DEFINED IMPULSIVE NEUTRAL FUNCTIONAL DIFFERENTIAL INCLUSIONS WITH NONLOCAL CONDITIONS

In this paper,using a fixed point theorem for condensing multi-valued maps,we investigate the existence of integral solutions to a class of nondensely defined neutral evolution impulsive differential inclusions with nonlocal conditions in Banach spaces.

(k, n-k) CONJUGATE MULTI-POINT BOUNDARY VALUE PROBLEMS FOR A CLASS OF HIGHER-ORDER DIFFERENTIAL INCLUSIONS

In this paper a fixed point theorem for contracting maps is used to investigate the existence of solutions to a class of higher-order differential inclusions with (k, n-k) conjugate multi-point boundary value problem.

Existence Results for Functional Differential Inclusions with Infinite Delay

The aim of the present paper is to investigate the existence of solutions to functional differential inclusions with infinite delay in Banach spaces. A relevant set of phase space axioms is proposed. The main tools used in this paper are certain fixed point theorems based on the setcontraction theory.

Existence Theorems for Periodic Differential Inclusions in IR^N

We study the periodic problem for differential inclusions in R^N.First we look for extremal periodicsolutions.Using techniques from multivalued analysis and a fixed point argument we establish an existencetheorem under some general hypotheses.We also consider the“nonconvex periodic problem”under lowersemicontinuity hypotheses,and the“convex periodic problem”under general upper semicontinuity hypotheseson the multivalued vector field.For both problems,we prove existence theorems under very general hypotheses.Our approach extends existing results in the literature and appear to be the most general results on the nonconvexperiodic problem.

EXISTENCE OF SOLUTIONS TO DIFFERENTIALINCLUSIONS IN BANACH SPACES

In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end ,the existence theorem of solutions to differential inclusions is obtained.

Adaptive saturated tracking control for solid launch vehicles in ascending based on differential inclusion stabilization

The large-range uncertainties of specific impulse,mass flow per second,aerodynamic coefficients and atmospheric density during rapid turning in solid launch vehicles(SLVs) ascending leads to the deviation of the actual trajectory from the reference one.One of the traditional trajectory tracking methods is to observe the uncertainties by Extended State Observer(ESO) and then modify the control commands.However,ESO cannot accurately estimate the uncertainties when the uncertainty ranges are large,which reduces the guidance accuracy.This paper introduces differential inclusion(DI) and designs a controller to solve the large-range parameter uncertainties problem.When above uncertainties have large ranges,it can be combined with the ascent dynamic equation and described as a DI system in the mathematical form of a set.If the DI system is stabilized,all the subsets are stabilized.Different from the traditional controllers,the parameters of the designed controller are calculated by the uncertain boundaries.Therefore,the controller can solve the problem of large-range parameter uncertainties of in ascending.Firstly,the ascent deviation system is obtained by linearization along the reference trajectory.The trajectory tracking system with engine parameters and aerodynamic uncertainties is described as an ascent DI system with respect to state deviation,which is called DI system.A DI adaptive saturation tracking controller(DIAST) is proposed to stabilize the DI system.Secondly,an improved barrier Lyapunov function(named time-varying tangent-log barrier Lyapunov function) is proposed to constrain the state deviations.Compared with traditional barrier Lyapunov function,it can dynamically adjust the boundary of deviation convergence,which improve the convergence rate and accuracy of altitude,velocity and LTIA deviation.In addition,the correction amplitudes of angle of attack(AOA) and angle of sideslip(AOS) need to be limited in order to guarantee that the overload constraint is not violated during actual flight.In this paper,a fixed time adaptive saturation compensation auxiliary system is designed to shorten the saturation time and accelerate the convergence rate,which eliminates the adverse effects caused by the saturation.Finally,it is proved that the state deviations are ultimately uniformly bounded under the action of DIAST controller.Simulation results show that the DI ascent tracking system is stabilized within the given uncertainty boundary values.The feasible bounds of uncertainty is broadened compared with Integrated Guidance and Control algorithm.Compared with Robust Gain-Scheduling Control method,the robustness to the engine parameters are greatly improved and the control variable is smoother.

On Fractional Differential Inclusion for an EpidemicModel via L-Fuzzy Fixed Point Results

The real world is filled with uncertainty,vagueness,and imprecision.The concepts we meet in everyday life are vague rather than precise.In real-world situations,if a model requires that conclusions drawn from it have some bearings on reality,then two major problems immediately arise,viz.real situations are not usually crisp and deterministic;complete descriptions of real systems often require more comprehensive data than human beings could recognize simultaneously,process and understand.Conventional mathematical tools which require all inferences to be exact,are not always efficient to handle imprecisions in a wide variety of practical situations.Following the latter development,a lot of attention has been paid to examining novel L-fuzzy analogues of conventional functional equations and their various applications.In this paper,new coincidence point results for single-valued mappings and an L-fuzzy set-valued map in metric spaces are proposed.Regarding novelty and generality,the obtained invariant point notions are compared with some well-known related concepts via non-trivial examples.It is observed that our principal results subsume and refine some important ones in the corresponding domains.As an application,one of our results is utilized to discussmore general existence conditions for realizing the solutions of a non-integer order inclusion model for COVID-19.

MULTIVALUED DIFFERENTIAL EQUATIONS IN BANACH SPACES AND THEIR APPLICATIONS

This paper studies the existence of solutions to a class of multivalued differential equations by using a surjectivity result for multivalued (S+) type mappings. The authors then apply their results to evolution hemivariational inequalities and parabolic equations with nonmonotone discontinuities, which generalize and extend previously known theorems.

On the Approximation Solvability of the Abstract Differential Inclusion

The approximation solvability of the abstract differential inclusion du/dt∈f(t,u) is presented. The convergence of the approximation solution and the existence of the solution for abstract evolution multivalued problem are discussed.