Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for generalized fractional integrals
Copyright policy )Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for generalized fractional integrals
In this paper we obtain the Hermite-Hadamard and Hermite-Hadamard-Fej��r type inequalities for fractional integrals which generalize the two familiar fractional integrals namely, the Riemann-Liouville and the Hadamard fractional integrals into a single form. We prove that, in most cases, we obtain the Riemann--Liouville and the Hadamard equivalence just by taking limits when a parameter $��\rightarrow 1$ and $��\rightarrow 0^+$, respectively.
Accepted Manuscript. 14 pages, Journal of Mathematical Analysis and Applications (2016)
- University of Delaware United States
convexity, 26A33, 26D10, 26D15, Hermite-Hadamard inequalities, Hermite-Hadamard-Fejér inequalities, Fractional derivatives and integrals, Katugampola fractional integral, Mathematics - Classical Analysis and ODEs, Hadamard fractional integral, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inequalities for sums, series and integrals, Riemann-Liouville fractional integral
convexity, 26A33, 26D10, 26D15, Hermite-Hadamard inequalities, Hermite-Hadamard-Fejér inequalities, Fractional derivatives and integrals, Katugampola fractional integral, Mathematics - Classical Analysis and ODEs, Hadamard fractional integral, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inequalities for sums, series and integrals, Riemann-Liouville fractional integral
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