Cauchy problem for differential equation with regularized Prabhakar fractional derivative

In this short note, we want to give the main parts of the verification of the ordered Prabhakar fractional order differential operator and the Cauchy problem for an equation with singular coefficients. That is, we present the exact solution of the Cauchy problem for the Prabhakar fractional derivative partial differential equation. Using the Fourier method, we find the general solution of the given equation. The unknown coefficient is found using the Hankel transformation. We have also presented important statements the bivariate MittagLeffler function E2 (x; y) and the Bessel function. The main objective is the Cauchy problem for a singular coefficient equation involving ordered Prabhakar derivatives. We present here the proof algorithm and a brief description of the main steps.