Estimations of the Disparity Between Hydrogen Ion Concentration and pH in the Context of Caputo–Fabrizio Fractional Integrals via Convexity

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Abstract
Fractional calculus is unique due to the fact it is as old as regular (integer) calculus, but it has also expanded its applications in a variety of fields and on a diversity of topics over the course of the last century. This leads to a continuous increase in the number of researchers and papers, ranging from integral inequality to biological models and then to systems with delay, neutrals, hybrids, etc. In this interplay between experts from various fields and mathematicians themselves, who employ these techniques in their theoretical research, the applications have increased. This research study focuses on the Caputo–Fabrizio operators because of its numerous applications. A set of generalized Hermite–Hadamard‐type inequalities for the Caputo–Fabrizio integrals is constructed via ( α , s , m )‐convex function. For the trapezoidal formula, errors are estimated. Moreover, the disparity between the expected (average) hydrogen ion concentration and pH is estimated in the present investigation. The accuracy of main conclusion is further affirmed by providing examples and graphical representations. In the framework of integral inequalities, this paper shows how the findings strengthen and illuminate a significant amount of earlier work.

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