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In this paper, we study the time optimal control of a class of partial stochastic impulsive functional differential systems with pseudo almost periodic coefficients in the α-norm functional spaces....

In this paper, we give sufficient conditions for the globally exponential stability of p-mean piecewise pseudo almost periodic mild solutions of a class of impulsive partial stochastic differential equations with infinite delay in Hilbert spaces. Our working tools are based on the fixed-point theorem for condensing maps combined with theory of operator semigroups and the stochastic analysis techniques. To illustrate our main result, we study the globally exponential stability of the neutral stochastic model arising in physical systems with infinite delay.

This paper investigates the time optimal control for a class of non-instantaneous impulsive Clarke subdifferential type stochastic evolution inclusions in Hilbert spaces. We focus first on the existence of mild solutions for these systems by using the measure of non-compactness and a fixed-point theorem wth the properties of Clarke subdifferential. Then, the existence of time optimal control of governed by stochastic control systems is also obtained. We do not assume that the evolution operator and the values of multi-valued map are compact. Finally, an example is given to illustrate the effectiveness of the results.

This paper concerns the Stepanov-like pseudo almost periodicity in distribution for a stochastic process and optimal control. Using the analytic semigroup theory, fractional power operators, stocha...

This paper is mainly concerned with the Stepanov-like pseudo almost periodicity to a class of impulsive perturbed partial stochastic differential equations. Firstly, we prove the existence of p-mean piecewise Stepanov-like pseudo almost periodic mild solutions for the impulsive stochastic dynamical system in a Hilbert space under non-Lipschitz conditions. The results are obtained by using the fixed point techniques with fractional power arguments. Then the existence of optimal pairs of system governed by impulsive partial stochastic differential equations is also obtained. Finally, an example is provided to illustrate the developed theory.

By using the Fourier transform method combining with the weighted energy method and some new skills, the global stability of oscillatory traveling waves for a monostable delayed equation is established. Particularly, the nonlinearity is nonlocal in the equation.

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochast...

Objective: in this article, we discuss the approximate controllability problems of a new class of fractional impulsive stochastic partial integro-differential systems in separable Hilbert s...

In this paper, we study optimal controls of a class of impulsive partial stochastic differential equations with weighted pseudo almost periodic coefficients in Hilbert spaces. Firstly, using interp...

In this paper, we introduce a new class of impulsive multi-valued stochastic delay differential equations with nonlocal conditions in separable Hilbert spaces. Using stochastic analysis, analytic semigroup, fractional powers of closed operators and suitable fixed point theorems, we prove the existence of optimal mild solutions for these systems in the $$\alpha $$ -norm. An example is provided to illustrate the applicability of our results.

In this paper, we study the piecewise pseudo almost periodicity in distribution for a stochastic process. Using the analytic semigroup theory and fixed point strategy with stochastic analysis theor...

This paper investigates the time optimal control problems to a new class of fractional non-instantaneous impulsive stochastic partial differential inclusions with Clarke subdifferential in Hilbert spaces. Firstly, using the fractional calculus, properties of fractional resolvent operators and a fixed-point theorem, the existence of mild solutions for these systems is presented. Secondly, the existence of time optimal control of system governed by fractional stochastic control inclusions with Clarke subdifferential and non-instantaneous impulses is also obtained. Finally, an example is given to illustrate our main results.

In this paper, we consider the optimization problems of exact controllability for a new class of fractional impulsive partial stochastic differential systems with state-dependent delay in Hilbert spaces. By utilizing suitable fixed point approach without imposing severe compactness condition on the operators, the theory of analytic sectorial operators, stochastic analysis, and the Hausdorff measure of noncompactness, some sufficient conditions are derived for achieving the required results. Finally, an example is provided to illustrate the obtained theory.

In this paper, we introduce a new class of multi-valued impulsive stochastic partial functional integrodifferential equations with infinite delay in the $$\alpha $$ -norm. Using stochastic analysis, analytic semigroup and fixed point strategy with the properties of fractional powers of closed operators, we establish the existence and uniqueness results of mild solutions for these equations with not instantaneous impulse. Then, the existence of optimal mild solutions is also proved. Particularly, the compactness of the operator semigroups is not needed. Finally, an example to illustrate the applications of main results is given.

In this paper, we establish a new composition theorem for pseudo almost periodic functions under non-Lipschitz conditions. We apply this new composition theorem together with a fixed-point theorem for condensing maps to investigate the existence of p $p$ -mean piecewise pseudo almost periodic mild solutions for a class of impulsive nonautonomous partial functional stochastic evolution equations in Hilbert spaces, and then, the exponential stability of p $p$ -mean piecewise pseudo almost periodic mild solutions is studied. Finally, an example is given to illustrate our results.

This paper is concerned with the pseudo almost periodic in distribution mild solutions for impulsive non-autonomous stochastic differential equations with unbounded delay and optimal controls in Hilbert spaces. Firstly, a suitable pseudo almost periodic in distribution mild solutions is introduced. The existence of pseudo almost periodic in distribution mild solutions are proved by means of a fixed-point theorem for condensing maps combined with stochastic analysis theory and evolution family. Secondly, the existence of optimal pairs of system governed by impulsive non-autonomous stochastic differential equations is also presented. Finally, an example is given for demonstration.

In this paper, we give sufficient conditions for the exponential stability of pseudo almost periodic in distribution mild solutions for nonautonomous impulsive neutral partial stochastic ev...

In this paper, we study a general class of impulsive partial stochastic differential equations with infinite delay and pseudo almost periodic coefficients in Hilbert spaces. Firstly, a more appropriate concept of pseudo almost periodic in distribution for stochastic processes of infinite class is introduced. Secondly, the existence of pseudo almost periodic in distribution mild solutions is investigated by utilizing the interpolation theory, the stochastic analysis techniques and fixed point theorem. The existence of optimal mild solutions of the systems is also proved. Finally, an example is provided to show the effectiveness of the theoretical results.

In this paper, a new class of fractional impulsive stochastic partial integro-differential control systems with state-dependent delay and their optimal controls in a Hilbert space is studied. We firstly prove an existence result of mild solutions for the control systems by using stochastic analysis, analytic \(\alpha \)-resolvent operator, fractional powers of closed operators and suitable fixed point theorems. Then we derive the existence conditions of optimal pairs to the fractional impulsive stochastic control systems. Finally, an example is given to illustrate the effectiveness of our main results.

In this paper, we establish the existence of optimal controls of systems governed by a class of fractional impulsive partial neutral stochastic integro-differential systems with infinite delay in a Hilbert space. The approaches used are fixed point theorem, stochastic analysis theory, and approximation technique combined with properties of the solution operator. Finally, an example is discussed to illustrate the efficiency of the results.

In this article, we consider a class of fractional impulsive multivalued stochastic partial integrodifferential equations with state-dependent delay in a real separable Hilbert space. Sufficient conditions for the complete controllability of impulsive fractional stochastic evolution systems are established by means of the fixed-point theorem for discontinuous multivalued operators due to Dhage and properties of the α $\alpha$ -resolvent operator combined with approximation techniques. Two examples are also given to illustrate the obtained theorem.

In this paper, the existence and asymptotic stability in p-th moment of mild solutions to a class of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay in Hilbert spaces is considered. By using H?lder?s inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdorff measure of noncompactness, a new set of sufficient conditions is formulated which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. These conditions do not require the nonlinear terms are assumed to be Lipschitz continuous. An example is also discussed to illustrate the efficiency of the obtained results.

In this paper, the approximate controllability of a new class of multi-valued fractional impulsive stochastic partial integro-differential equations with infinite delay in Hilbert spaces is studied. Firstly, by using stochastic analysis, analytic α-resolvent operator, fractional powers of closed operators and a fixed point theorem for multi-valued maps, we prove an existence result of mild solutions for the control systems under the mixed Lipschitz and Caratheodory conditions. Secondly, we discuss a new set of sufficient conditions for the approximate controllability of the systems. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is provided to illustrate the proposed theory.

In this paper, we study a new class of fractional nonlinear impulsive stochastic integro-differential equations with infinite delay in separable Hilbert spaces. Firstly, by using the measure of noncompactness, stochastic analysis theory, solution operators and suitable fixed point theorems, we prove the existence of mild solutions for these systems. Secondly, the existence of optimal mild solutions is obtained. Thirdly, we establish the controllability of the controlled fractional impulsive stochastic functional integro-differential systems with not instantaneous impulses. Finally, an example is provided to show the application of our results.

In this paper, we study a new class of impulsive stochastic partial integro-differential inclusions with state-dependent delay in separable Hilbert spaces. Firstly, by using stochastic analysis theory, analytic resolvent operators, fractional powers of closed operators and suitable fixed point theorems, we prove the existence of mild and extremal mild solutions for these systems in the α-norm. Secondly, we establish the controllability of the controlled stochastic partial integro-differential inclusions with not instantaneous impulses. The results are obtained under the mixed Lipschitz and Caratheodory conditions. Finally, an example is provided to show the application of our results.

In this article, the approximate controllability of fractional impulsive partial neutral stochastic differential inclusions with state-dependent delay and fractional sectorial operators in Hilbert spaces is studied. By using the stochastic analysis, the fractional sectorial operators and a fixed point theorem for multi-valued maps combined with approximation techniques, we discuss a new set of sufficient conditions for the approximate controllability of the systems under the mixed Lipschitz and Caratheodory conditions. An example is provided to illustrate the obtained theory.

In this paper, we study optimal control problems for a class of fractional stochastic functional differential equations of order \(\alpha \in (1, 2]\) in Hilbert spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence of mild solutions are investigated by using the fractional calculus, stochastic analysis theory, and fixed point theorems with the strongly continuous \(\alpha \)-order cosine family. Then, the existence conditions of optimal pairs of systems governed by a fractional stochastic partial differential equations of order \(\alpha \in (1, 2]\) with infinite delay are presented. The results are obtained under the mixed Lipschitz and Caratheodory conditions. Finally, an example is presented to illustrate the main results.

This paper is mainly concerned with a new class of fractional impulsive partial stochastic integro-differential equations with state-dependent delay and optimal controls in Hilbert spaces. Firstly, a more appropriate concept for mild solutions is introduced. Secondly, existence and uniqueness of mild solutions are proved by means of stochastic analysis theory, fractional calculus and the fixed point technique combined with solution operator. The existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. Finally, an example is given for demonstration.

In this paper, we introduce the optimal control problems governed by a new class of impulsive stochastic partial neutral evolution equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, the analytic semigroup theory, fractional powers of closed operators, and suitable fixed point theorems, we prove an existence result of mild solutions for the control systems in the α-norm without the assumptions of compactness. Next, we derive the existence conditions of optimal pairs of these systems. Finally, application to a nonlinear impulsive stochastic parabolic optimal control system is considered.

In this paper, we consider a new class of non-instantaneous impulsive partial stochastic differential systems with fractional sectorial operators in separable Hilbert spaces. Using the fractional calculus, the measure of noncompactness, properties of sectorial operators and fixed point theorems, we establish the optimal controllability to the these control systems without assuming the operators is compact. Finally, an example is provided to illustrate the obtained theory.

In this paper, we introduce a new class of impulsive stochastic partial neutral functional integro-differential equations with infinite delay and not instantaneous impulses in separable Hilbert spaces. We prove the existence of mild solutions for these equations in the -norm without the assumptions of compactness. The results are obtained using suitable fixed point theorems with the properties of analytic resolvent operators. Finally, an example is presented to illustrate the theory.

In this paper, a new class of fractional impulsive partial neutral stochastic integro-differential equations with infinite delay is introduced.Under some dissipative conditions, we obtain the existence, uniqueness and continuous dependence of mild solutions for these equations. An application involving a fractional stochastic parabolic system with not instantaneous impulses is considered.

In this paper, the approximate controllability of a class of fractional stochastic neutral integro-differential inclusions with infinite delay in Hilbert spaces is considered. By using the Holder inequality, the -resolvent operator and fixed point strategy, a new set of necessary and sufficient conditions are formulated which guarantees the approximate controllability of the nonlinear fractional stochastic system. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is provided to illustrate the proposed theory.

We study the approximate controllability of partial fractional neutral stochastic functional integro-differential inclusions with state-dependent delay under the assumptions that the corresponding linear system is approximately controllable. Using fractional calculus, stochastic analysis theory, and the fixed-point technique with the properties of analytic \(\alpha \)-resolvent operators, a new set of sufficient conditions for approximate controllability of fractional stochastic functional integro-differential inclusions are formulated and proved. The results in this paper are generalization and continuation of the recent results on this issue. An example is provided to show the application of our result.

In this paper, the existence of mild solutions for a class of impulsive fractional partial neutral functional integro-differential inclusions with infinite delay and analytic α-resolvent operators in Banach spaces is investigated. Sufficient conditions for the existence are derived with the help of the fixed-point theorem for discontinuous multi-valued operators due to Dhage and the fractional power of operators combined with approximation techniques. An example is provided to illustrate the theory.

We study the approximate controllability of a class of fractional partial neutral integro-differential inclusions with infinite delay in Hilbert spaces. By using the analytic α-resolvent operator and the fixed point theorem for discontinuous multivalued operators due to Dhage, a new set of necessary and sufficient conditions are formulated which guarantee the approximate controllability of the nonlinear fractional system. The results are obtained under the assumption that the associated linear system is approximately controllable. An example is provided to illustrate the main results.

We prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state-dependent delay in an abstract space. Sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using the Krasnoselskii–Schaefer type fixed point theorem with the fractional power of operators. An example is provided to illustrate the main results.