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arXiv · 1806.00477

Fractional Sensitivity Equation Method: Applications to Fractional Model Construction

Ehsan Kharazmi·Mohsen Zayernouri
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Abstract

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.

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Ehsan Kharazmi, Mohsen Zayernouri. 2018-05-31. Fractional Sensitivity Equation Method: Applications to Fractional Model Construction. https://arxiv.org/abs/1806.00477

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