## Scientific Bulletin. Physical and Mathematical Research

#### Abstract

In the work a Cauchy-Goursta problem has been formulated and investigated for a second kind degenerated equation of hyperbolic type. During the investigation, it was used properties of Gauss’s hyper geometric function and symbol of Pochhammer, the considered problem equivalently reduced to an integral equation with respect to trace of unknown function. Properties of Riemann-Liuvill integral-differential and generalized integral-differential operators have found solution of the taken integral equation. To find solution of the problem it was used general solution of the equation. A class of generalized solutions was introduced for the correctness of the problem. It was found necessary conditions for the given functions.

#### First Page

76

#### Last Page

83

#### DOI

517.98

#### References

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[10] Urinov A.K., Usmonov D.A.(2020) On the representation of the general solution of a degenerate hyperbolic equation of the second kind. Materials of the International Scientific Conference “Modern Problems of Differential Equations and Related Sections of Mathematics”, Part I: Fergana. Pp. 161-162.

#### Recommended Citation

Usmonov, Doniyor
(2021)
"A Cauchy-Goursat problem for a second kind degenerated equation of hyperbolic type,"
*Scientific Bulletin. Physical and Mathematical Research*: Vol. 3
:
Iss.
1
, Article 12.

DOI: 517.98

Available at:
https://uzjournals.edu.uz/adu/vol3/iss1/12