Common Fixed Point Theorems on <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"><a:mi>S</a:mi></a:math>-Metric Spaces for Integral Type Contractions Involving Rational Terms and Application to Fractional Integral Equation

It has been shown that the findings of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"><a:mi>d</a:mi></a:math> -metric spaces may be deduced from <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"><c:mi>S</c:mi></c:math> -metric spaces by considering <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M4"><e:mi>d</e:mi><e:mfenced open="(" close=")"><e:mrow><e:mi>ϖ</e:mi><e:mo>,</e:mo><e:mi>ϰ</e:mi></e:mrow></e:mfenced><e:mo>=</e:mo><e:mi>Λ</e:mi><e:mfenced open="(" close=")"><e:mrow><e:mi>ϖ</e:mi><e:mo>,</e:mo><e:mi>ϖ</e:mi><e:mo>,</e:mo><e:mi>ϰ</e:mi></e:mrow></e:mfenced></e:math> . In this study, no such concepts that translate to the outcomes of metric spaces are considered. We establish standard fixed point theorems for integral type contractions involving rational terms in the context of complete <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" id="M5"><k:mi>S</k:mi></k:math> -metric spaces and discuss their implications. We also provide examples to illustrate the work. This paper’s findings generalize and expand a number of previously published conclusions. In addition, the abstract conclusions are supported by an application of the Riemann-Liouville calculus to a fractional integral problem and a supportive numerical example.