Oscillation of solutions to a generalized forced nonlinear conformable fractional differential equation

A M Ogunbanjo,P O Arawomo

doi:10.22199/issn.0717-6279-2019-03-0028

Abstract

By using averaging functions, we present some new oscillation criteria for the solution of a generalized forced nonlinear conformable fractional differential equation. The results obtained here extend and improve on some existing results. Examples are also given to show the validity of our results.

Highlights

In recent years there had been an increasing interest in fractional calculus because of its many applications in Science and Engineering see [5, 6, 9, 13] and references therein
Several researchers have worked on the oscillation of second order dynamic, sublinear and superlinear differential equations but not many have worked on oscillation of factional differential equations and the few have used Caputo, Riemann-Liouville and Modified RiemannLiouville such fractional derivatives see [3, 11, 12, 14, 15]
Ntouyas [7] have worked on the oscillation of conformable fractional differential equations

Summary

Introduction

In recent years there had been an increasing interest in fractional calculus because of its many applications in Science and Engineering see [5, 6, 9, 13] and references therein. Ntouyas [7] have worked on the oscillation of conformable fractional differential equations. With the definition of conformable fractional derivative given by R. Khalil [8], we consider the establishment of oscillation of solutions to the generalized forced nonlinear conformable fractional differential equation If f is α-differentiable in some (0, a), a > 0, and limt→0+ f α(t) exists, define f α(0) = lim f α(t)

Results

Conclusion