| Summary: | Fractional <i>q</i>-calculus plays an extremely important role in mathematics and physics. In this paper, we aim to investigate the existence of triple-positive solutions for nonlinear singular fractional <i>q</i>-difference equation boundary value problems at resonance by means of the fixed-point index theorem and the <i>q</i>-Laplace transform, where the nonlinearity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo></mrow></semantics></math></inline-formula> permits singularities at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>t</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>=</mo><mi>v</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>. The obtained theorem is well illustrated with the aid of an example.
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