This Special Issue aims to provide advanced developments in the applications of fractional calculus in various problems of stochastic mechanics with emphasis on risk evaluation and uncertainty quantification. It is composed of eight papers written by researchers and academics from China, Germany, Italy, Spain and United Kingdom. The papers cover theoretical issues, computational methods and modeling techniques of structures and external agencies in order to refine the actual methods used in practical engineering problems, with particular regards to the stochastic mechanics context. In particular, there are some new results about the solution of barrier problem of noisy dynamical system embedded with fractional derivative, the estimation of the random temperature effects in the viscoelastic behavior of hereditary materials, the parametric study of stochastic variation of the fractional Laplacian order in the non-local structural element, the exact evaluation of response fractional spectral moments of linear fractional oscillators excited by a white noise, the path integral method for non-linear system under Levy white noise, the use of fractional operators in the interval analysis, the stochastic dynamical analysis of primary suspension in railway vehicle modeled by fractional operators, and the analysis of non-local viscoelastic nano-rod forced by Gaussian noise.
**TOPICS:**
Structural elements (Construction), Viscoelasticity, Path integrals, Noise (Sound), Temperature effects, Dynamic systems, Modeling, Nonlinear systems, China, Nanorods, Risk assessment, White noise, Railway vehicles, Computational methods, Risk, Uncertainty quantification