Obtaining a representation of the solution to the Cauchy problem for equation high-order fractional derivative, by the method of finding self-similar solutions

TL;DR

This paper develops a method to find solutions to high-order fractional differential equations by leveraging self-similar solutions, specifically addressing the Cauchy problem for equations with Riemann-Liouville derivatives of order between 1 and 2.

Contribution

It introduces a novel approach using self-similar solutions to solve the Cauchy problem for high-order fractional equations with Riemann-Liouville derivatives.

Findings

Successfully obtained solutions for the Cauchy problem using self-similar methods.

Extended the understanding of fractional differential equations of even order.

Provided a framework applicable to similar high-order fractional problems.

Abstract

In this paper, with the help of previously constructed self-similar solutions, a solution of the Cauchy problem for an equation of even order with a fractional Riemann-Liouville derivative of order $1<\alpha<2$ is obtained.