INITIAL-BOUNDARY PROBLEM FOR DIFFERENTIAL EQUATIONS WITH FRACTIONAL DERIVATIVES OF HIGHER ORDER IN THE SOBOLEV CLASS

Abstract

Due to the large applicability of fractional equations to physical, technical, and biological processes, scientists around the world are increasingly interested in the study of higher-order equations involving fractional derivatives. Today, the study and solution of initial boundary value problems for higher-order mixed-type equations involving fractional derivatives has become an urgent task. In this work, the initial-boundary value problem in a cylindrical domain for a partial differential equation involving a fractional derivative in the Miller-Ross sense and the initial-boundary value problem for a higher-order fractional differential equation in the Sobolev class are investigated. Spherical functions are a method that allows us to find solutions to problems in mathematical physics more simply, easily, and quickly. With the help of these functions, it is possible to easily find solutions to even more complex problems.