| Summary: | The Caputo–Fabrizio fractional integral operator is one of the important notions of fractional calculus. It is involved in numerous illustrative and practical issues. The main goal of this paper is to investigate weighted fractional integral inequalities using the Caputo–Fabrizio fractional integral operator with non-singular <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>e</mi><mrow><mo>−</mo><mfenced separators="" open="(" close=")"><mfrac><mrow><mn>1</mn><mo>−</mo><mi>δ</mi></mrow><mi>δ</mi></mfrac></mfenced><mrow><mo>(</mo><mi>ϰ</mi><mo>−</mo><mi>s</mi><mo>)</mo></mrow></mrow></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>δ</mi><mo><</mo><mn>1</mn></mrow></semantics></math></inline-formula>. Furthermore, based on a family of <i>n</i> positive functions defined on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo></mrow></semantics></math></inline-formula>, we investigate some new extensions of weighted fractional integral inequalities.
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