Unique solvability of a non‐local problem for mixed‐type equation with fractional derivative |
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| Authors: | Erkinjon T Karimov Abdumauvlen S Berdyshev Nilufar A Rakhmatullaeva |
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| Affiliation: | 1. Department of Mathematics and Statistics, Sultan Qaboos University, Muscat, Oman;2. Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan;3. Kazakh National Pedagogical University named after Abai, Almaty, Kazakhstan;4. Tashkent State Technical University, Tashkent, Uzbekistan |
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| Abstract: | In this work, we investigate a boundary problem with non‐local conditions for mixed parabolic–hyperbolic‐type equation with three lines of type changing with Caputo fractional derivative in the parabolic part. We equivalently reduce considered problem to the system of second kind Volterra integral equations. In the parabolic part, we use solution of the first boundary problem with appropriate Green's function, and in hyperbolic parts, we use corresponding solutions of the Cauchy problem. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | Caputo fractional derivative mixed‐type equation Volterra integral equation parabolic– hyperbolic‐type equation Green's function |
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