TY - JOUR AU - O. Kh. Abdullaev PY - 2019/06/25 Y2 - 2024/03/28 TI - On the problem for the mixed-type degenerate equation with Caputo and Erdelyi – Kober operators of fractional order JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 71 IS - 6 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1471 AB - UDC 517.9 We establish the existence and uniqueness of the solution of a local problem for the degenerate parabolic-hyperbolic-typeequations 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 theexistence and uniqueness of solution of the investigated problem. ER -