Geodesic
Integral inequalities in fractional calculus with general analytic kernels
Filomat, Tome 37 (2023) no. 11, p. 3659

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DOI

Many different definitions of fractional calculus have been proposed in the literature, especially in recent years, and these can be classified into groups with similar properties. Many recent papers have studied inequalities for fractional integrals of particular types of functions, such as Hermite-Hadamard inequalities and related results. Here we provide theorems valid for a whole general class of fractional operators (anything defined using an integral with an analytic kernel function), so that it is no longer necessary to prove such results for each model one by one. We consider several types of fractional integral inequalities, which apply to functions of convex and synchronous type, and extend them to the full generality of fractional calculus with analytic kernels.
DOI : 10.2298/FIL2311659M
Classification : 26A33, 26D10, 26D15
Keywords: Fractional integrals, Hermite-Hadamard inequality, Integral inequalities, General analytic kernels, Convexity 
Pshtiwan Othman Mohammed; Arran Fernandez. Integral inequalities in fractional calculus with general analytic kernels. Filomat, Tome 37 (2023) no. 11, p. 3659 . doi: 10.2298/FIL2311659M
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     title = {Integral inequalities in fractional calculus with general analytic kernels},
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     year = {2023},
     volume = {37},
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     doi = {10.2298/FIL2311659M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2311659M/}
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