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Dirichlet problem for the generalized Laplace equation with the Caputo derivative

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Abstract

For a partial differential equation with the Caputo fractional derivative with respect to one of two independent variables, we solve the Dirichlet problem in a rectangular domain. The considered equation becomes the Laplace equation if the order of the fractional derivative is equal to 2. By using a method based on the completeness of the system of eigenfunctions of the Sturm-Liouville problem, we prove the uniqueness of the solution.

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Authors and Affiliations

  1. Research Institute for Applied Mathematics and Automation, Kabardino-Balkar Scientific Center, Russian Academy of Science, Nalchik, Russia

    O. Kh. Masaeva

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  1. O. Kh. Masaeva
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Original Russian Text © O.Kh. Masaeva, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 3, pp. 442–446.

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Masaeva, O.K. Dirichlet problem for the generalized Laplace equation with the Caputo derivative. Diff Equat 48, 449–454 (2012). https://doi.org/10.1134/S0012266112030184

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  • DOI: https://doi.org/10.1134/S0012266112030184

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