An inverse problem for Hilfer type differential equation of higher order

Abstract

In three-dimensional domain, an identification problem of the source function for Hilfer type partial differential equation of the even order with a condition in an integral form and with a small positive parameter in the mixed derivative is considered. The solution of this fractional differential equation of a higher order is studied in the class of regular functions. The case, when the order of fractional operator is 0 < α < 1, is studied. The Fourier series method is used and a countable system of ordinary differential equations is obtained. The nonlocal boundary value problem is integrated as an ordinary differential equation. By the aid of given additional condition, we obtained the representation for redefinition (source) function. Using the Cauchy–Schwarz inequality and the Bessel inequality, we proved the absolute and uniform convergence of the obtained Fourier series.