The oscillatory solutions of multi-order fractional differential equations

TL;DR

This paper analyzes the asymptotic behavior of multi-order fractional differential equations, providing theoretical insights and numerical validation for oscillatory solutions using advanced mathematical tools.

Contribution

It introduces a systematic approach combining spectral analysis and comparison principles to study oscillatory solutions of complex fractional differential equations.

Findings

Established conditions for oscillatory behavior

Validated theoretical results with numerical examples

Extended understanding of multi-order fractional dynamics

Abstract

This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional differentiable functions, the comparison principle, counterfactual reasoning, and the spectral analysis method (concerning the integral presentations of basic solutions). Some numerical examples are also provided to demonstrate the validity of the proposed results.