| Summary: | This paper aims to improve Hille oscillation criteria for the third-order functional dynamic equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mfenced separators="" open="{" close="}"><msub><mi>p</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><msub><mi>ϕ</mi><msub><mi>γ</mi><mn>2</mn></msub></msub><mfenced separators="" open="(" close=")"><msup><mfenced separators="" open="[" close="]"><msub><mi>p</mi><mn>1</mn></msub><mfenced open="(" close=")"><mi>ξ</mi></mfenced><msub><mi>ϕ</mi><msub><mi>γ</mi><mn>1</mn></msub></msub><mfenced separators="" open="(" close=")"><msup><mi>y</mi><mo>Δ</mo></msup><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow></mfenced></mfenced><mo>Δ</mo></msup></mfenced></mfenced><mo>Δ</mo></msup><mo>+</mo><mi>a</mi><mrow><mo>(</mo><mi>ξ</mi><mo>)</mo></mrow><msub><mi>ϕ</mi><mi>γ</mi></msub><mfenced separators="" open="(" close=")"><mi>y</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>ξ</mi><mo>)</mo><mo>)</mo></mfenced><mo>=</mo><mn>0</mn><mo>,</mo></mrow></semantics></math></inline-formula> on an above-unbounded time scale <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="double-struck">T</mi></semantics></math></inline-formula>. The obtained results improve related contributions reported in the literature without restrictive conditions on the time scales. To demonstrate the essential results, an example is presented.
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