A comprehensive study on Milne-type inequalities with tempered fractional integrals. (English) Zbl 1541.26042
Summary: In the framework of tempered fractional integrals, we obtain a fundamental identity for differentiable convex functions. By employing this identity, we derive several modifications of fractional Milne inequalities, providing novel extensions to the domain of tempered fractional integrals. The research comprehensively examines significant functional classes, including convex functions, bounded functions, Lipschitzian functions, and functions of bounded variation.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
| 26D07 | Inequalities involving other types of functions |
Keywords:
inequalities of Milne type; fractional version; tempered fractional integrals; convex functionsReferences:
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