ON THE PROBLEM FOR A MIXED-TYPE DEGENERATE EQUATION WITH CAPUTO AND ERDELYI-KOBER OPERATORS OF FRACTIONAL ORDER

被引：9
|
作者：
Abdullaev, O. Kh. [1 ]
机构：
[1] Uzbekistan Natl Univ, Tashkent, Uzbekistan
来源：
UKRAINIAN MATHEMATICAL JOURNAL | 2019年 / 71卷 / 06期
关键词：
D O I：
10.1007/s11253-019-01682-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We establish the existence and uniqueness of the solution of a local problem for the degenerate parabolic-hyperbolic-type equations with loaded terms containing the trace of solution in the Erdelyi-Kober integrals. Since the trace of solution (i.e., u(x, 0)) is contained in the Erdelyi-Kober integrals and the hyperbolic equation is degenerated in the line y = 0, the existence and uniqueness of solution of the investigated problem are proved by using the properties of hypergeometric functions, the estimates for these functions, and certain integral equalities.
引用
收藏
页码：825 / 842
页数：18
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