The oscillatory solutions of multi-order fractional differential equations

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.

Figures (4)

• Figure 1: The orbit of the solution to equation \ref{['vd']} with the initial condition $x_0 = 1$ on the interval $[0,70]$.
• Figure 2: The orbit of the solution to equation \ref{['bsvd1']} with the initial condition $x_0 = 1$ on the interval $[0,80]$.
• Figure 3: The orbit of the solution to equation \ref{['4.3.41']} with the initial condition $x(0) = -0.5$ on the interval $[0,150]$.
• Figure 4: The orbit of the solution to equation \ref{['4.3.59']} with the initial condition $x(0) = 0.6$ on the interval $[0,150]$.

Theorems & Definitions (56)

• Lemma 2.1
• proof
• Lemma 2.2
• proof
• Lemma 2.3
• proof
• Definition 2.4
• Lemma 2.5
• proof
• Lemma 2.6