On the fractional counterpart of the higher-order equations

TL;DR

This paper investigates solutions to fractional higher-order equations, exploring special cases with integer derivatives, and expressing solutions via stable subordinators and inverse processes, establishing links between fractional and classical higher-order equations.

Contribution

It introduces explicit solutions to fractional higher-order equations using stable subordinators and their inverses, and clarifies the relationship between fractional and traditional higher-order equations.

Findings

Explicit solutions expressed through stable subordinators.

Connections established between fractional and classical higher-order equations.

Analysis of special cases with integer derivatives.

Abstract

In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be expressed by means of the transition laws of stable subordinators and their inverse processes. In particular we establish connections between fractional and higher-order equations.