Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for generalized fractional integrals ☆
By Hua Chen, Udita N. Katugampola. 2016
227 citations recorded by the source corpus.
Abstract In this paper we obtain the Hermite–Hadamard and Hermite–Hadamard–Fejer 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 ρ → 1 and ρ → 0 + , respectively.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/53bc00cd0e5c4eec56bc0559413f32cb41c7c163
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In Applied Mathematics
- Fahd Jarad
- Thabet Abdeljawad
- Saima Rashid
- Muhammad Aslam Noor
- Dumitru Băleanu
- Udita N. Katugampola
- Shin Min Kang
- Y. Chu
Citations in the corpus
- Bounds of Riemann-Liouville Fractional Integrals in General Form via Convex Functions and Their Applications (2018, methodology): “if we take h(z) = z ρ ρ , ρ > 0 it reduces to the left-sided and right-sided Katugampola fractional integrals given in [11], 4.”
- New fractional integral unifying six existing fractional integrals (2016, background): “s of 2ndkind and a recurrence formula for such sequences. Further applications of Katugampola fractional integrals or derivatives are in probability theory [1], variational calculus [2], inequalities [9], Langevin equations [34], Fourier and Laplace transforms [20] fractional differential equations [”
- Some Estimates for Generalized Riemann-Liouville Fractional Integrals of Exponentially Convex Functions and Their Applications (2019, background): “References 1.”