| Summary: | In this paper, we first establish two right-quantum integral equalities involving a right-quantum derivative and a parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>∈</mo><mo> </mo><mfenced separators="" open="[" close="]"><mn>0</mn><mo>,</mo><mn>1</mn></mfenced></mrow></semantics></math></inline-formula>. Then, we prove modified versions of Simpson’s and Newton’s type inequalities using established equalities for right-quantum differentiable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="(" close=")"><mi>α</mi><mo>,</mo><mi>m</mi></mfenced></semantics></math></inline-formula>-convex functions. The newly developed inequalities are also proven to be expansions of comparable inequalities found in the literature.
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