Solution of the problem with initial conditions for the equation high-order fractional Hilfer derivative

TL;DR

This paper develops a method to solve initial value problems for high-order equations involving Hilfer fractional derivatives using self-similar solutions.

Contribution

It introduces a novel approach to construct solutions for high-order fractional differential equations with Hilfer derivatives.

Findings

Successfully constructs solutions for the Cauchy problem

Extends methods for fractional differential equations

Provides a framework for future research in fractional calculus

Abstract

In this paper, with the help of previously constructed self-similar solutions, we construct a solution to a Cauchy-type problem for an even-order high-order equation with a fractional derivative in the sense of Hilfer