In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with ...In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.展开更多
Control systems governed by linear time-invariant neutral equations with different fractional orders are considered. Sufficient and necessary conditions for the controllability of those systems are established. The ex...Control systems governed by linear time-invariant neutral equations with different fractional orders are considered. Sufficient and necessary conditions for the controllability of those systems are established. The existence of optimal controls for the systems is given. Finally, two examples are provided to show the application of our results.展开更多
Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel cha...Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.展开更多
After the discovery of fraction quantum Hall states in the 1980s, it became more and more clear that Landau symmetry breaking theory does not describe all possible quantum phases of matter. The new quan- tum phases of...After the discovery of fraction quantum Hall states in the 1980s, it became more and more clear that Landau symmetry breaking theory does not describe all possible quantum phases of matter. The new quan- tum phases of matter were called topologically ordered phases（for gapped cases） or quantum ordered phases （for gapless cases）, which correspond to pat- terns of many-body entanglement. One may won- der： besides quantum Hall systems, are there other systems that realize the new topological/quantum order？展开更多
In this paper, we will establish the sufficient conditions for the oscillation of solutions of neutral time fractional partial differential equation of the form for where Ω??is a bounded domain in RN with a ...In this paper, we will establish the sufficient conditions for the oscillation of solutions of neutral time fractional partial differential equation of the form for where Ω??is a bounded domain in RN with a piecewise smooth boundary ?is a constant, is the Riemann-Liouville fractional derivative of order a?of u with respect to t and is the Laplacian operator in the Euclidean N-space RN subject to the展开更多
In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establis...In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establish the existence and uniqueness of the S-asymptotically periodic α-mild solutions. The linear part generates a compact and exponentially stable analytic semigroup and the nonlinear parts satisfy some conditions with respect to the fractional power norm of the linear part, which greatly improve and generalize the relevant results of existing literatures.展开更多
The absolute amounts and relative distributions of neutral nitrogen compounds in the Tabei oilfield (e.g. blocks Ln1-Ln11) showed remarkable migration fractionation in the vertical direction. From Ordovician reservoir...The absolute amounts and relative distributions of neutral nitrogen compounds in the Tabei oilfield (e.g. blocks Ln1-Ln11) showed remarkable migration fractionation in the vertical direction. From Ordovician reservoirs (O) to oil legs T-Ⅲ and T-Ⅰ of Triassic reservoirs in blocks LN1-LN11, the concentrations of + decreased from {1.59}μg/g, {0.49}μg/g to {0.17}μg/g (oil). The ratios of various alkylcarbazole isomers, such as 1,8-dimethylcarbazole/nitrogen-partially shielded isomers and 1,8-dimethylcarbazole/nitrogen-exposed isomers, were adopted as the indicators of petroleum migration. The ratios increased from {0.13}, {0.20} to {0.67} and from {0.42}, {0.87} to {3.30}, corresponding to those of Ordovician oil leg and oil legs T-Ⅲ and T-Ⅰ. In going from the south to the north of the Tabei oilfield, the absolute concentrations of neutral nitrogen compounds decreased drastically, and the nitrogen-shielded isomers were enriched relative to nitrogen-exposed isomers and nitrogen-partially shielded isomers. Crude oils in the Tabei oilfield migrated laterally from the Jilake structure to the Sangtamu fault uplift and Lunnan fault uplift, and crude oils in the same fault uplift migrated and remigrated vertically from Ordovician reservoirs, to oil legs T-Ⅲ to T-Ⅰ of Triassic reservoirs.展开更多
In this paper, we consider a class of Sobolev-type fractional neutral stochastic differential equations driven by fractional Brownian motion with infinite delay in a Hilbert space. When α>1-H, by the ...In this paper, we consider a class of Sobolev-type fractional neutral stochastic differential equations driven by fractional Brownian motion with infinite delay in a Hilbert space. When α>1-H, by the technique of Sadovskii’s fixed point theorem, stochastic calculus and the methods adopted directly from deterministic control problems, we study the approximate controllability of the stochastic system.展开更多
This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the ...This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.展开更多
A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis th...A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.展开更多
In this paper, we study the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of class r for fractional integro-differential neutral equations. An example is presented to illustrate the ap...In this paper, we study the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of class r for fractional integro-differential neutral equations. An example is presented to illustrate the application of the abstract results.展开更多
In this paper, we are concerned with a class of neutral fractional stochastic partial differential equations driven by a Rosenblatt process. By the stochastic analysis technique, the properties of operator semigroup a...In this paper, we are concerned with a class of neutral fractional stochastic partial differential equations driven by a Rosenblatt process. By the stochastic analysis technique, the properties of operator semigroup and combining the Banach fixed-point theorem, we prove the existence and uniqueness of the mild solutions to this kind of equations driven by Rosenblatt process. In the end, an example is given to demonstrate the theory of our work.展开更多
In this paper, we study a class of doubly perturbed neutral stochastic functional equations driven by fractional Brownian motion. Under some non-Lipschitz conditions, we will prove the existence and uniqueness of the ...In this paper, we study a class of doubly perturbed neutral stochastic functional equations driven by fractional Brownian motion. Under some non-Lipschitz conditions, we will prove the existence and uniqueness of the solution to these equations by providing a semimartingale approximation of a fractional stochastic integration.展开更多
In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the exi...In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.展开更多
This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt pro-cess.We discuss t...This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt pro-cess.We discuss the sufficient conditions for approximate controllability and null controllability for Hilfer fractional neutral stochastic partial differential equations driven by Rosenblatt process.Finally,we provide two examples to verify the obtained results.展开更多
文摘In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.
基金supported by the Science and Technology Planning Project(2014JQ1041)of Shaanxi Provincethe Scientic Research Program Funded by Shaanxi Provincial Education Department(14JK1300)+1 种基金the Research Fund for the Doctoral Program(BS1342)of Xi’an Polytechnic Universitysupported by Ministerio de Economíay Competitividad and EC fund FEDER,Project no.MTM2010-15314,Spain
文摘Control systems governed by linear time-invariant neutral equations with different fractional orders are considered. Sufficient and necessary conditions for the controllability of those systems are established. The existence of optimal controls for the systems is given. Finally, two examples are provided to show the application of our results.
文摘Asymptotic stability of linear and interval linear fractional-order neutral delay differential systems described by the Caputo-Fabrizio (CF) fractional derivatives is investigated. Using Laplace transform, a novel characteristic equation is derived. Stability criteria are established based on an algebraic approach and norm-based criteria are also presented. It is shown that asymptotic stability is ensured for linear fractional-order neutral delay differential systems provided that the underlying stability criterion holds for any delay parameter. In addition, sufficient conditions are derived to ensure the asymptotic stability of interval linear fractional order neutral delay differential systems. Examples are provided to illustrate the effectiveness and applicability of the theoretical results.
文摘After the discovery of fraction quantum Hall states in the 1980s, it became more and more clear that Landau symmetry breaking theory does not describe all possible quantum phases of matter. The new quan- tum phases of matter were called topologically ordered phases（for gapped cases） or quantum ordered phases （for gapless cases）, which correspond to pat- terns of many-body entanglement. One may won- der： besides quantum Hall systems, are there other systems that realize the new topological/quantum order？
文摘In this paper, we will establish the sufficient conditions for the oscillation of solutions of neutral time fractional partial differential equation of the form for where Ω??is a bounded domain in RN with a piecewise smooth boundary ?is a constant, is the Riemann-Liouville fractional derivative of order a?of u with respect to t and is the Laplacian operator in the Euclidean N-space RN subject to the
基金Supported by NNSF of China(11871302)China Postdoctoral Science Foundation(2020M682140)+1 种基金NSF of Shanxi,China (201901D211399)Graduate Research Support project of Northwest Normal University(2021KYZZ01030)
文摘In this paper, we investigate a class of abstract neutral fractional delayed evolution equation in the fractional power space. With the aid of the analytic semigroup theories and some fixed point theorems, we establish the existence and uniqueness of the S-asymptotically periodic α-mild solutions. The linear part generates a compact and exponentially stable analytic semigroup and the nonlinear parts satisfy some conditions with respect to the fractional power norm of the linear part, which greatly improve and generalize the relevant results of existing literatures.
文摘The absolute amounts and relative distributions of neutral nitrogen compounds in the Tabei oilfield (e.g. blocks Ln1-Ln11) showed remarkable migration fractionation in the vertical direction. From Ordovician reservoirs (O) to oil legs T-Ⅲ and T-Ⅰ of Triassic reservoirs in blocks LN1-LN11, the concentrations of + decreased from {1.59}μg/g, {0.49}μg/g to {0.17}μg/g (oil). The ratios of various alkylcarbazole isomers, such as 1,8-dimethylcarbazole/nitrogen-partially shielded isomers and 1,8-dimethylcarbazole/nitrogen-exposed isomers, were adopted as the indicators of petroleum migration. The ratios increased from {0.13}, {0.20} to {0.67} and from {0.42}, {0.87} to {3.30}, corresponding to those of Ordovician oil leg and oil legs T-Ⅲ and T-Ⅰ. In going from the south to the north of the Tabei oilfield, the absolute concentrations of neutral nitrogen compounds decreased drastically, and the nitrogen-shielded isomers were enriched relative to nitrogen-exposed isomers and nitrogen-partially shielded isomers. Crude oils in the Tabei oilfield migrated laterally from the Jilake structure to the Sangtamu fault uplift and Lunnan fault uplift, and crude oils in the same fault uplift migrated and remigrated vertically from Ordovician reservoirs, to oil legs T-Ⅲ to T-Ⅰ of Triassic reservoirs.
文摘In this paper, we consider a class of Sobolev-type fractional neutral stochastic differential equations driven by fractional Brownian motion with infinite delay in a Hilbert space. When α>1-H, by the technique of Sadovskii’s fixed point theorem, stochastic calculus and the methods adopted directly from deterministic control problems, we study the approximate controllability of the stochastic system.
文摘This paper is concerned with the approximate controllability of nonlinear fractional impulsive neutral stochastic integro-differential equations with nonlocal conditions and infinite delay in Hilbert spaces under the assumptions that the corresponding linear system is approximately controllable. By the Krasnoselskii-Schaefer-type fixed point theorem and stochastic analysis theory, some sufficient conditions are given for the approximate controllability of the system. At the end, an example is given to illustrate the application of our result.
基金by the National Natural Science Foundation of China(Nos.11871162,11661050,11561059).
文摘A class of fractional stochastic neutral functional differential equation is analyzed in this paper.With the utilization of the fractional calculations,semigroup theory,fixed point technique and stochastic analysis theory,a sufficient condition of the existence for p-mean almost periodic solution is obtained,which are supported by two examples.
基金supported by National Natural Science Foundation of China(Grant Nos.11271379 and 11671406)
文摘In this paper, we study the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of class r for fractional integro-differential neutral equations. An example is presented to illustrate the application of the abstract results.
文摘In this paper, we are concerned with a class of neutral fractional stochastic partial differential equations driven by a Rosenblatt process. By the stochastic analysis technique, the properties of operator semigroup and combining the Banach fixed-point theorem, we prove the existence and uniqueness of the mild solutions to this kind of equations driven by Rosenblatt process. In the end, an example is given to demonstrate the theory of our work.
文摘In this paper, we study a class of doubly perturbed neutral stochastic functional equations driven by fractional Brownian motion. Under some non-Lipschitz conditions, we will prove the existence and uniqueness of the solution to these equations by providing a semimartingale approximation of a fractional stochastic integration.
基金financed by NSF of Anhui Province (090416237)NNSF of China (10971229)+4 种基金the 211 Project of Anhui University (02303129 KJTD002B)the Foundation of Anhui Education Bureau(KJ2009A49 KJ2009AZ005)Research Fund for the Doctoral Program of Higher Education(20103401120002)
文摘In this paper, we consider the existence of mild solution to a class of neutral fractional differential equations with infinite delay. By means of fixed points methods, we obtain some sufficient conditions for the existence and uniqueness of mild solutions, which extend some known results.
文摘This manuscript is mainly focusing on the approximate controllability and the null controllability for fractional neutral stochastic partial differential equations with delay driven by Rosenblatt pro-cess.We discuss the sufficient conditions for approximate controllability and null controllability for Hilfer fractional neutral stochastic partial differential equations driven by Rosenblatt process.Finally,we provide two examples to verify the obtained results.
