Oscillation Theorems for Fractional Order Neutral Differential Equations
|Published in:||Issue 2, (Vol. 10) / 2016|
|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 𝑫𝒕𝜶[𝒓(𝒕)[𝑫𝒕𝜶(𝒙(𝒕)+𝒑(𝒕)𝒙(𝝉(𝒕)))]𝜸]+𝒒(𝒕)𝒙𝜸𝜸(𝝈(𝒕))=𝟎, where 𝑫𝒕𝜶(⋅) 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 𝟐𝜶-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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