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Unique solvability of a non‐local problem for mixed‐type equation with fractional derivative
Author(s) -
Karimov Erkinjon T.,
Berdyshev Abdumauvlen S.,
Rakhmatullaeva Nilufar A.
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4215
Subject(s) - mathematics , fractional calculus , type (biology) , boundary value problem , hyperbolic partial differential equation , mathematical analysis , function (biology) , cauchy problem , parabolic partial differential equation , work (physics) , derivative (finance) , initial value problem , partial differential equation , mechanical engineering , ecology , evolutionary biology , financial economics , engineering , economics , biology
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.