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In this paper, we make use of the Riemann–Liouville fractional <i>q</i>-integral operator to discuss the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>S</mi><mrow><mi>q</mi><mo>,</mo><mi>δ</mi></mrow><mo>*</mo></msubsup><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> of univalent functions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>></mo><mn>0</mn><mo>,</mo><mi>α</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi><mo>−</mo><mo>{</mo><mn>0</mn><mo>}</mo></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mo>|</mo><mi>q</mi><mo>|</mo><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Then, we develop convolution results for the given class of univalent functions by utilizing a concept of the fractional <i>q</i>-difference operator. Moreover, we derive the normalized classes <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">P</mi><mrow><mi>δ</mi><mo>,</mo><mi>q</mi></mrow><mi>ζ</mi></msubsup><mrow><mo>(</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">P</mi><mrow><mi>δ</mi><mo>,</mo><mi>q</mi></mrow></msub><mrow><mo>(</mo><mi>β</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mo>|</mo><mi>q</mi><mo>|</mo><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi><mo>≥</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>≤</mo><mi>β</mi><mo>≤</mo><mn>1</mn><mo>,</mo><mi>ζ</mi><mo>></mo><mn>0</mn><mo>)</mo></mrow></semantics></math></inline-formula> of analytic functions on a unit disc and provide conditions for the parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>,</mo><mi>δ</mi><mo>,</mo><mi>ζ</mi><mo>,</mo><mi>β</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> so that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi mathvariant="script">P</mi><mrow><mi>δ</mi><mo>,</mo><mi>q</mi></mrow><mi>ζ</mi></msubsup><mrow><mo>(</mo><mi>β</mi><mo>,</mo><mi>γ</mi><mo>)</mo></mrow><mo>⊂</mo><msubsup><mi>S</mi><mrow><mi>q</mi><mo>,</mo><mi>δ</mi></mrow><mo>*</mo></msubsup><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">P</mi><mrow><mi>δ</mi><mo>,</mo><mi>q</mi></mrow></msub><mrow><mo>(</mo><mi>β</mi><mo>)</mo></mrow><mo>⊂</mo><msubsup><mi>S</mi><mrow><mi>q</mi><mo>,</mo><mi>δ</mi></mrow><mo>*</mo></msubsup><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi><mo>−</mo><mo>{</mo><mn>0</mn><mo>}</mo></mrow></semantics></math></inline-formula>. Finally, we also propose an application to symmetric <i>q</i>-analogues and Ruscheweh’s duality theory.