Oscillation Theorems for Fractional Order Neutral Differential Equations
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 re...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Stefan cel Mare University of Suceava
2016-10-01
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| Series: | Journal of Applied Computer Science & Mathematics |
| Subjects: | |
| Online Access: | http://jacsm.ro/view/?pid=22_7 |
| Summary: | 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.
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| ISSN: | 2066-4273 2066-3129 |