This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained b...This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.展开更多
The controllability of a class of conformable fractional differential system with a non-densely defined linear part satisfying Hille-Yosida condition,is discussed.The existence of mild solution and controllability is ...The controllability of a class of conformable fractional differential system with a non-densely defined linear part satisfying Hille-Yosida condition,is discussed.The existence of mild solution and controllability is established by Banach-fixed point theorem for the system with non-local conditions and control term appearing also in the nonlinear part.An example is discussed to illustrate the results.展开更多
基金supported by Ministry of Human Resource and Development(MHR-02-23-200-429/304)
文摘This paper has two sections which deals with a second order stochastic neutral partial differential equation with state dependent delay. In the first section the existence and uniqueness of mild solution is obtained by use of measure of non-compactness. In the second section the conditions for approximate controllability are investigated for the distributed second order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert space. Our method is an extension of co-author N. Sukavanam’s novel approach in [22]. Thereby, we remove the need to assume the invertibility of a controllability operator used by authors in [5], which fails to exist in infinite dimensional spaces if the associated semigroup is compact. Our approach also removes the need to check the invertibility of the controllability Gramian operator and associated limit condition used by the authors in [20], which are practically difficult to verify and apply. An example is provided to illustrate the presented theory.
文摘The controllability of a class of conformable fractional differential system with a non-densely defined linear part satisfying Hille-Yosida condition,is discussed.The existence of mild solution and controllability is established by Banach-fixed point theorem for the system with non-local conditions and control term appearing also in the nonlinear part.An example is discussed to illustrate the results.
