MULTI-TERM TIME-FRACTIONAL DERIVATIVE HEAT EQUATION FOR ONE-DIMENSIONAL DUNKL OPERATOR

In this paper, we investigate the well-posedness for Cauchy problem multi-term time-fractional heat equation associated with Dunkl operator. The under consideration includes a linear combination of Caputo derivatives in time decreasing orders (0, 1) and positive constant coefficients one-dimensional operator.  To show solvability problem  use several important properties multinomial Mittag-Leffler functions transforms, since various estimates follow from explicit solutions form these special transforms. Then prove uniqueness existence results. achieve our goals, methods corresponding to different areas mathematics such as theory partial differential equations, mathematical physics, hypoelliptic operators functional analysis. particular, direct inverse transform establish on Sobolev space. generalized are studied.