Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

TL;DR

This paper studies the existence, uniqueness, and asymptotic behavior of solutions for linear systems of multi-order fractional differential equations, providing series representations and qualitative insights.

Contribution

It offers new fundamental results on existence, uniqueness, and asymptotic analysis specific to multi-order fractional differential systems.

Findings

Established existence and uniqueness theorems.

Derived series solutions for homogeneous systems.

Characterized asymptotic behavior of solutions.

Abstract

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of linear multi-order fractional differential equation systems.