On Time-Fractional Diffusion Equations with Space-Dependent Variable Order

By Yavar Kian, É. Soccorsi, Masahiro Yamamoto. Annales de l'Institute Henri Poincare. Physique theorique, 2017

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This paper deals with mathematical problems related to space-dependent anomalous diffusion processes. Namely, we investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We establish that variable-order time-fractional Cauchy problems admit a unique weak solution and prove that the space-dependent variable-order coefficient is uniquely determined by the knowledge of a suitable time sequence of partial initial-boundary maps.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c07b5619c04c2a374ff12b3c91c1fa9de4f03d30