Paper title: Oscillation Theorems for Fractional Order Neutral Differential Equations
DOI: https://doi.org/10.4316/JACSM.201602007
Published in: Issue 2, (Vol. 10) / 2016Download
Publishing date: 2016-10-20
Pages: 46-51
Author(s): GANESAN Vellaiyappaudaiyar, KUMAR Sathish M.
Abstract. The purpose of this paper is to study the oscillation of the fractional order neutral differential equation ๐‘ซ๐’•๐œถ[๐’“(๐’•)[๐‘ซ๐’•๐œถ(๐’™(๐’•)+๐’‘(๐’•)๐’™(๐‰(๐’•)))]๐œธ]+๐’’(๐’•)๐’™๐œธ๐œธ(๐ˆ(๐’•))=๐ŸŽ, where ๐‘ซ๐’•๐œถ(โ‹…) is a modified Riemann-Liouville derivative. The obtained results are based on the new comparison theorems, which enable us to reduce the oscillatory problem of ๐Ÿ๐œถ-order fractional differential equation to the oscillation of the first order equation. The results are easily verified.
Keywords: Oscillation; Comparison Theorem; Fractional Differential Equation; Modified Riemann-Liouville Derivative
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