Asymptotic Separation of Solutions to Fractional Stochastic Multi-Term Differential Equations

In this paper, we study the exact asymptotic separation rate of two distinct solutions of Caputo stochastic multi-term differential equations (Caputo SMTDEs). Our goal in this paper is to establish results of the global existence and uniqueness and continuity dependence of the initial values of the solutions to Caputo SMTDEs with non-permutable matrices of order α∈(12,1) and β∈(0,1) whose coefficients satisfy a standard Lipschitz condition. For this class of systems, we then show the asymptotic separation property between two different solutions of Caputo SMTDEs with a more general condition based on λ. Furthermore, the asymptotic separation rate for the two distinct mild solutions reveals that our asymptotic results are general.

Eigen-transitions in cantilever cylindrical shells subjected to vertical edge loads

A thin cantilever cylindrical shell subjected to a transverse shear force at the free end can experience two distinct modes of buckling, depending on its relative thickness and length. If the former parameter is fixed, then a short cylinder buckles in a diffuse manner, while the eigenmodal deformation of a moderately long shell is localised, both axially and circumferentially, near its fixed end. Donnell-type buckling equations for cylindrical shells are here coupled with a non-symmetric membrane basic state to produce a linear boundary-value problem that is shown to capture the transition between the aforementioned instability modes. The main interest lies in exploring the approximate asymptotic separation of the independent variables in the corresponding stability equations, when the eigen-deformation is doubly localised. Comparisons with direct numerical simulations of the full buckling problem provide further insight into the accuracy and limitations of our approximations.