In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hi...In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.展开更多
A dedicated key server cannot be instituted to manage keys for MANETs since they are dynamic and unstable. The Lagrange's polynomial and curve fitting are being used to implement hierarchical key management for Mo...A dedicated key server cannot be instituted to manage keys for MANETs since they are dynamic and unstable. The Lagrange's polynomial and curve fitting are being used to implement hierarchical key management for Mobile Ad hoc Networks(MANETs). The polynomial interpolation by Lagrange and curve fitting requires high computational efforts for higher order polynomials and moreover they are susceptible to Runge's phenomenon. The Chebyshev polynomials are secure, accurate, and stable and there is no limit to the degree of the polynomials. The distributed key management is a big challenge in these time varying networks. In this work, the Chebyshev polynomials are used to perform key management and tested in various conditions. The secret key shares generation, symmetric key construction and key distribution by using Chebyshev polynomials are the main elements of this projected work. The significance property of Chebyshev polynomials is its recursive nature. The mobile nodes usually have less computational power and less memory, the key management by using Chebyshev polynomials reduces the burden of mobile nodes to implement the overall system.展开更多
文摘In this work,the optimal control for a class of Hilfer fractional stochastic integrodifferential systems driven by Rosenblatt process and Poisson jumps has been discussed in infinite dimensional space involving the Hilfer fractional derivative.First,we study the existence and uniqueness of mild solution results are proved by the virtue of fractional calculus,successive approximation method and stochastic analysis techniques.Second,the optimal control of the proposed problem is presented by using Balder’s theorem.Finally,an example is demonstrated to illustrate the obtained theoretical results.
文摘A dedicated key server cannot be instituted to manage keys for MANETs since they are dynamic and unstable. The Lagrange's polynomial and curve fitting are being used to implement hierarchical key management for Mobile Ad hoc Networks(MANETs). The polynomial interpolation by Lagrange and curve fitting requires high computational efforts for higher order polynomials and moreover they are susceptible to Runge's phenomenon. The Chebyshev polynomials are secure, accurate, and stable and there is no limit to the degree of the polynomials. The distributed key management is a big challenge in these time varying networks. In this work, the Chebyshev polynomials are used to perform key management and tested in various conditions. The secret key shares generation, symmetric key construction and key distribution by using Chebyshev polynomials are the main elements of this projected work. The significance property of Chebyshev polynomials is its recursive nature. The mobile nodes usually have less computational power and less memory, the key management by using Chebyshev polynomials reduces the burden of mobile nodes to implement the overall system.
