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Title: Operator-Based Uncertainty Quantification of Stochastic Fractional Partial Differential Equations
Abstract Fractional calculus provides a rigorous mathematical framework to describe anomalous stochastic processes by generalizing the notion of classical differential equations to their fractional-order counterparts. By introducing the fractional orders as uncertain variables, we develop an operator-based uncertainty quantification framework in the context of stochastic fractional partial differential equations (SFPDEs), subject to additive random noise. We characterize different sources of uncertainty and then, propagate their associated randomness to the system response by employing a probabilistic collocation method (PCM). We develop a fast, stable, and convergent Petrov–Galerkin spectral method in the physical domain in order to formulate the forward solver in simulating each realization of random variables in the sampling procedure.  more » « less
Award ID(s):
1923201
PAR ID:
10213731
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Verification, Validation and Uncertainty Quantification
Volume:
4
Issue:
4
ISSN:
2377-2158
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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