Cauchy problem for fractional high order equation with singular coefficient

Abstract

In this paper, we aim to study the Cauchy problem posed for a fractional order equation. General solution of the time-fractional equation is found by the Fourier method. The solution to the given problem is shown to be unique using the generalized Hankel transform. The solution consists of the Bessel function and the Mittag-Leffler function. Unknown coefficients are found by Hankel transformation. It is shown that the constructed solution satisfies the initial condition and equation.