TY - JOUR
AU - O. Kh. Abdullaev
PY - 2019/06/25
Y2 - 2020/12/05
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 - http://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 -