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<p>In this paper, an analog of the Tricomi problem for a mixed-type equation is investigated, which in one part of the mixed domain is a fractional telegraph equation with Riemann-Liouville derivatives, and in the other part it is a degenerate hyperbolic equation of the first kind. Using the Tricomi method, the uniqueness of the solution to the problem under study is proven. The proof of the existence of a solution is equivalently reduced to the question of the solvability of the Fredholm integral equation of the second kind.</p>

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AN ANALOG OF THE TRICOMI PROBLEM FOR A DEGENERATE EQUATION OF MIXED TYPE WITH FRACTIONAL DERIVATIVES

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Murat O. Mamchuev,
  • Rakhim T. Zunnunov

摘要

In this paper, an analog of the Tricomi problem for a mixed-type equation is investigated, which in one part of the mixed domain is a fractional telegraph equation with Riemann-Liouville derivatives, and in the other part it is a degenerate hyperbolic equation of the first kind. Using the Tricomi method, the uniqueness of the solution to the problem under study is proven. The proof of the existence of a solution is equivalently reduced to the question of the solvability of the Fredholm integral equation of the second kind.