New Fractional Variants of Hermite-Hadamard type Inequalities with Applications to Shannon Entropy via Exponential Distributions
DOI:
https://doi.org/10.26713/cma.v17i3.3620Keywords:
Convex functions, Hermite-Hadamard inequality,, AB-fractional operatorsAbstract
This article offers an attractive new link between fractional calculus, convex functions, and special functions by establishing fractional integral inequalities using Raina's function. We obtain new Hermite-Hadamard inequalities using the Atangana-Baleanu fractional integral operator. Sharper, more sophisticated versions of these results are then driven by a recently developed fractional lemma. Real-world impact is demonstrated by applications to Shannon entropy under the exponential distribution. Given the increasing importance of Mittag-Leffler and Raina-type functions, a thorough reference review is provided to help readers get a sense of this quickly changing field. The results provide significant breakthroughs that open up new avenues for the discipline and provide new insights.
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bibitem{ref1}
M.A. Latif, H. Kalsoom, M.Z. Abidin,
Hermite--Hadamard-type inequalities involving harmonically convex function via the Atangana--Baleanu fractional integral operator,
textit{Symmetry}, textbf{14}(9) (2022), 1774.
bibitem{ref2}
S. Kermausuor, E.R. Nwaeze,
New fractional integral inequalities via $k$-Atangana--Baleanu fractional integral operators,
textit{Fractal Fract.}, textbf{7}(10) (2023), 740.
bibitem{ref3}
H. Kavurmac{i} "Onalan, et al.,
On new general versions of Hermite--Hadamard type integral inequalities via fractional integral operators with Mittag-Leffler kernel,
textit{J. Inequal. Appl.}, textbf{2021} (2021), 186.
bibitem{ref4}
M.A. Ard{i}c{c}, A.O. Akdemir, H. Kavurmac{i} "Onalan,
Integral inequalities for differentiable $s$-convex functions in the second sense via Atangana--Baleanu fractional integral operators,
textit{Filomat}, textbf{37}(18) (2023), 6229--6244.
bibitem{ref5}
c{S}. K{i}z{i}l, M.A. Ard{i}c{c},
Inequalities for strongly convex functions via Atangana--Baleanu integral operators,
textit{Turkish J. Sci.}, textbf{6}(2) (2021), 96--109.
bibitem{ref6}
E. Y"uksel,
Inequalities for strongly $s$-convex functions via Atangana--Baleanu fractional integral operators,
textit{Turk. J. Nat. Sci.}, textbf{13}(2) (2024), 49--60.
bibitem{ref7}
M. Tariq, H. Ahmad, S.K. Sahoo, A. Kashuri, T.A. Nofal, C.H. Hsu,
Inequalities of Simpson--Mercer-type including Atangana--Baleanu fractional operators and their applications,
textit{AIMS Math.}, textbf{7}(8) (2022), 15159--15181.
bibitem{ref8}
M. Tariq, S.K. Ntouyas, W. Afzal, J. Tariboon,
Some new approaches of integral inequalities involving Raina and Mittag--Leffler function pertaining to Atangana--Baleanu fractional integral operator,
textit{J. Math. Comput. Sci.}, textbf{41}(2) (2025), 244--263.
bibitem{ref9}
M. Tariq, S.K. Ntouyas, H. Ahmad, R. Efendiev,
Some new modifications of integral inequalities in the frame of AB fractional integral operator,
textit{Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. Math.}, textbf{46}(1) (2026), 1--22.
bibitem{ref10}
M. Tariq, S.K. Ntouyas, A.A. Shaikh,
A comprehensive review of the Hermite--Hadamard inequality pertaining to fractional integral operators,
textit{Mathematics}, textbf{11}(8) (2023), 1953.
bibitem{m_{5}}
C.P. Niculescu, L.E. Persson,
emph{Convex Functions and Their Applications},
Springer, New York, 2006.
bibitem{Hadamard}
J. Hadamard,
'{E}tude sur les propri'{e}t'{e}s des fonctions enti`{e}res en particulier d'une fonction consid'{e}r'{e}'{e} par Riemann,
textit{J. Math. Pures Appl.}, textbf{58} (1893), 171--215.
bibitem{RAina1}
R.K. Raina,
On generalized Wright's hypergeometric functions and fractional calculus operators,
textit{East Asian Math. J.}, textbf{21} (2005), 191--203.
bibitem{Z6}
M.J.V. Cortez, R. Liko, A. Kashuri, J.E.H. Hern'{a}ndez,
New quantum estimates of trapezium-type inequalities for generalized $phi$--convex functions,
textit{Mathematics}, textbf{7} (2019), 1047.
bibitem{Z06}
M.J.V. Cortez, A. Kashuri, J.E.-H. Hern'{a}ndez,
Trapezium-type inequalities for Raina's fractional integrals operator using generalized convex functions,
textit{Symmetry}, textbf{12} (2020), 1034.
bibitem{hijaz1}
H. Ahmad, M. Tariq, S.K. Sahoo, J. Baili, C. Cesarano,
New estimations of Hermite--Hadamard type integral inequalities for special functions,
textit{Fractal Fract.}, textbf{5} (2021), 144.
bibitem{m_{tnv}}
S. Varov{s}anec,
On $h$--convexity,
textit{J. Math. Anal. Appl.}, textbf{326} (2007), 303--311.
bibitem{QS4}
A. Atangana, D. Baleanu,
New fractional derivatives with non-local and non-singular kernel,
textit{Thermal Sci.}, textbf{20} (2016), 763--769.
bibitem{QS5}
T. Abdeljawad, D. Baleanu,
Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel,
textit{J. Nonlinear Sci. Appl.}, textbf{10} (2017), 1098--1107.
bibitem{MMA}
M. Tariq, S.K. Ntouyas, J. Tariboon,
Some new variants of fractional Hermite--Hadamard and Pachpatte-type integral inequalities involving Raina's and Mittag-Leffler functions with applications,
textit{J. Math. Comput. Sci.}, textbf{40} (2025), 415--443.
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