# On the problem for the mixed-type degenerate equation with Caputo and Erdelyi – Kober operators of fractional order

### Abstract

UDC 517.9We 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., $u(x, 0)$) appears in the Erdelyi – Kober integrals and the hyperbolic-type equation is degenerated in the line $y = 0$, we use some properties and estimates for hypergeometric functions and, in addition, some integral equalities in proving the existence and uniqueness of solution of the investigated problem.

Published

25.06.2019

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 71, no. 6, June 2019, pp. 723-38, http://umj.imath.kiev.ua/index.php/umj/article/view/1471.

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Section

Research articles