Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions

Abstract

This study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. The main aim is to unify the Beta Integral Lemma (Lemma 2) and the Gamma Integral Lemma (Lemma 3) into a single framework. By combining these two powerful tools, we propose new criteria that effectively characterize the asymptotic behavior of non-oscillatory solutions to the given equations. The analysis of such solutions has significant implications in the fields of oscillation and stability theory. Notably, our findings extend prior work by exploring a wider range of equations with more general functions and coefficients, thereby broadening the applicability and deepening the understanding of both asymptotic and oscillatory behaviors. Moreover, the criteria we introduce offer improvements over previous approaches, as demonstrated by the example provided, which highlights the advantages of our results in comparison to earlier methods.