  We introduce a class of fractional Dirac type operators with time-variable
coefficients by means of a Witt basis and the Riemann-Liouville fractional
derivative with respect to another function. Direct and inverse fractional
Cauchy type problems are studied for the introduced operators. We give explicit
solutions of the considered fractional Cauchy type problems. We also use a
recent method [17] to recover a variable coefficient solution of some inverse
fractional wave and heat type equations. Illustrative examples are provided.
