The Oscillatory of Linear Conformable Fractional Differential Equations of Kamenev Type

Hui Liu,Run Xu

doi:10.1155/2020/3857592

Abstract

In this paper, the oscillatory of the Kamenev-type linear conformable fractional differential equations in the form of ptyα+1tα+yα+1t+qtyt=0 is studied, where t≥t0 and 0<α≤1. By employing a generalized Riccati transformation technique and integral average method, we obtain some oscillation criteria for the equation. We also give some examples to illustrate the significance of our results.

Highlights

In 2014, a new definition, which is called the conformable derivative, was proposed in the literature [10], and the properties and calculations of conformable derivatives have been studied in the literature [11–14]
We discuss the oscillatory behavior about linear conformable fractional differential equations of Kamenev type of the following: Discrete Dynamics in Nature and Society
(D1): the left conformable fractional derivative starting from t0 of a function f: [t0, ∞) ⟶ R of order 0 < α ≤ 1 is defined by

Summary

Introduction

In 2014, a new definition, which is called the conformable derivative, was proposed in the literature [10], and the properties and calculations of conformable derivatives have been studied in the literature [11–14]. There is much about the oscillations of fractional differential equations [15–28] and the references therein), there is little about the conformable fractional differential equations of Kamenev type. In 2019, Shao and Zhaowen [14] established new oscillation criteria of Kamenev type for linear conformable of the above equation, where p ∈ C([t0, ∞), (0, ∞)), q ∈ C ([t0, ∞), R), 0 < α ≤ 1 and q might change signs.

Results

Conclusion