AN ANALOG OF THE TRICOMI PROBLEM FOR A MIXED TYPE EQUATION WITH RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_31Keywords:
parabolic-hyperbolic type equation, mixed domain, Tricomi problem, Cauchy problem, first boundary value problemAbstract
In this article, the Tricomi problem for a parabolic-hyperbolic type equation in a mixed domain is investigated. Riemann-Liouville fractional derivative participates in the parabolic part of the considerated equation, and the hyperbolic part consists of a degenerate hyperbolic equation of the second kind. The solution of the problem in the hyperbolic sub-domain is found as a solution to the Cauchy problem, and in a parabolic sub-domain as a solution to the first boundary value problem. For proving the existence of the solution of the problem, the theory of second kind Volterra integral equations is used.
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