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<p>In this paper, we investigate the unique solvability of a generalized Tricomi problem with an integral condition for a loaded equation involving a fractional operator. By analyzing the problem for a third-order equation with a telegraph operator, we extend the results to a generalized operator with small parameters. Furthermore, the integral condition in the parabolic region enables the generalization of local problems associated with second- and third-order equations.</p>

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Extension of the Tricomi problem for a third-order loaded parabolic-hyperbolic equation

  • 期刊论文

  • 发表日期：

    2025年3月8日

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  • Umida Baltaeva,
  • Marjona Sh. Kosimova,
  • Hamrobek Hayitbayev

摘要

In this paper, we investigate the unique solvability of a generalized Tricomi problem with an integral condition for a loaded equation involving a fractional operator. By analyzing the problem for a third-order equation with a telegraph operator, we extend the results to a generalized operator with small parameters. Furthermore, the integral condition in the parabolic region enables the generalization of local problems associated with second- and third-order equations.