Kharazmi, Ehsan; Zayernouri, Mohsen Fractional sensitivity equation method: application to fractional model construction. (English) Zbl 1448.35550 J. Sci. Comput. 80, No. 1, 110-140 (2019). Summary: Fractional differential equations provide a tractable mathematical framework to describe anomalous behavior in complex physical systems, yet they introduce new sensitive model parameters, i.e. derivative orders, in addition to model coefficients. We formulate a sensitivity analysis of fractional models by developing a fractional sensitivity equation method. We obtain the adjoint fractional sensitivity equations, in which we present a fractional operator associated with logarithmic-power law kernel. We further construct a gradient-based optimization algorithm to compute an accurate parameter estimation in fractional model construction. We develop a fast, stable, and convergent Petrov-Galerkin spectral method to numerically solve the coupled system of original fractional model and its corresponding adjoint fractional sensitivity equations. Cited in 8 Documents MSC: 35R11 Fractional partial differential equations 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 26A33 Fractional derivatives and integrals Keywords:sensitive fractional orders; model error; logarithmic-power law kernel; Petrov-Galerkin spectral method; iterative algorithm; parameter estimation Software:ADIFOR; ADIC PDFBibTeX XMLCite \textit{E. Kharazmi} and \textit{M. Zayernouri}, J. Sci. Comput. 80, No. 1, 110--140 (2019; Zbl 1448.35550) Full Text: DOI arXiv References: [1] West, B.J., Bologna, M., Grigolini, P.: Physics of Fractal Operators. 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