This work focuses on the existence and trajectory(T-)controllability of mixed fractional Brownian motion(fBm)with the Hurst index(1/2,1)and neutral stochastic integrodifferential equations(NSIDEs)with deviating argume...This work focuses on the existence and trajectory(T-)controllability of mixed fractional Brownian motion(fBm)with the Hurst index(1/2,1)and neutral stochastic integrodifferential equations(NSIDEs)with deviating argument and fBm.Stochastic integrodifferential equations(SIDEs)are solved in Hilbert space using stochastic analysis,the resolvent operator,and Krasnoselskii's fixed point theorem(KFPT).Furthermore,providing adequate assumptions,the T-controllability of the considered system is organised by using extended Gronwall's inequality.We demonstrate the theoretical insights and numerical simulations are included which is unique and makes this work more interesting.The obtained results generalise existing results from[Chalishajar,D.N.,George,R.K.,&Nandakumaran,A.K.(2010).Trajectory controllability of nonlinear integro-differential system.Journal of Franklin Institute,347(7),1065–1075.;Durga,N.,Muthukumar,P.,&Malik,M.(2022).Trajectory controllability of Hilfer fractional neutral stochastic differential equation with deviated argument and mixed fractional Brownian motion.Optimisation,1–27.;Muslim,M.,&George,R.K.(2019).Trajectory controllability of the nonlinear systems governed by fractional differential equations.Differential Equations and Dynamical Systems,27,529–537.;Dhayal,R.,Malik,M.,&Abbas,S.(2021).Approximate and trajectory controllability of fractional stochastic differential equation with non-instantaneous impulses and Poisson jumps.Asian Journal of Control,23(6),2669–2680.].展开更多
In this article,the authors set up an optimal control of neutral stochastic integro-differential equations(NSIDEs)driven by fractional Brownian motion(fBm)in a Hilbert space by using Grimmer resolvent operators.Suffic...In this article,the authors set up an optimal control of neutral stochastic integro-differential equations(NSIDEs)driven by fractional Brownian motion(fBm)in a Hilbert space by using Grimmer resolvent operators.Sufficient conditions for mild solutions are formulated and proved by using the Banach contraction mapping principle and stochastic analytic techniques.We have extended the problem in[Issaka et al.(2020)Results on nonlocal stochastic integro-differential equations are driven by a fractional Brownian motion.Open Mathematics,18(1),1097–1112]to NSIDEs driven by fBm and have used modified techniques to make them compatible with optimal controls of stochastic integro-differential systems.In addition,the optimal control of the proposed problem is presented using Balder's theorem.Such optimal control of NSIDEs with fBm is widely used in automatic control,aircraft and air traffic control,electrical networks,wavelet expansions,etc.Finally,an example illustrates the potential of the main results.展开更多
文摘This work focuses on the existence and trajectory(T-)controllability of mixed fractional Brownian motion(fBm)with the Hurst index(1/2,1)and neutral stochastic integrodifferential equations(NSIDEs)with deviating argument and fBm.Stochastic integrodifferential equations(SIDEs)are solved in Hilbert space using stochastic analysis,the resolvent operator,and Krasnoselskii's fixed point theorem(KFPT).Furthermore,providing adequate assumptions,the T-controllability of the considered system is organised by using extended Gronwall's inequality.We demonstrate the theoretical insights and numerical simulations are included which is unique and makes this work more interesting.The obtained results generalise existing results from[Chalishajar,D.N.,George,R.K.,&Nandakumaran,A.K.(2010).Trajectory controllability of nonlinear integro-differential system.Journal of Franklin Institute,347(7),1065–1075.;Durga,N.,Muthukumar,P.,&Malik,M.(2022).Trajectory controllability of Hilfer fractional neutral stochastic differential equation with deviated argument and mixed fractional Brownian motion.Optimisation,1–27.;Muslim,M.,&George,R.K.(2019).Trajectory controllability of the nonlinear systems governed by fractional differential equations.Differential Equations and Dynamical Systems,27,529–537.;Dhayal,R.,Malik,M.,&Abbas,S.(2021).Approximate and trajectory controllability of fractional stochastic differential equation with non-instantaneous impulses and Poisson jumps.Asian Journal of Control,23(6),2669–2680.].
文摘In this article,the authors set up an optimal control of neutral stochastic integro-differential equations(NSIDEs)driven by fractional Brownian motion(fBm)in a Hilbert space by using Grimmer resolvent operators.Sufficient conditions for mild solutions are formulated and proved by using the Banach contraction mapping principle and stochastic analytic techniques.We have extended the problem in[Issaka et al.(2020)Results on nonlocal stochastic integro-differential equations are driven by a fractional Brownian motion.Open Mathematics,18(1),1097–1112]to NSIDEs driven by fBm and have used modified techniques to make them compatible with optimal controls of stochastic integro-differential systems.In addition,the optimal control of the proposed problem is presented using Balder's theorem.Such optimal control of NSIDEs with fBm is widely used in automatic control,aircraft and air traffic control,electrical networks,wavelet expansions,etc.Finally,an example illustrates the potential of the main results.
