Fractional differential equations on Lie groups and submonoids

In the present work, we define generic fractional differential operators on Lie groups and their submonoids. Criteria of solvability and Fredholmness for fractional differential equations are established and fundamental solutions in case of operators with constant coefficients are provided. In the second part, we solve six distinct Cauchy initial value problems for degenerate diffusion equations with fractional Hadamard type derivatives in time.