Yıl 2022,
Cilt: 51 Sayı: 3, 775 - 786, 01.06.2022
Martin Bohner
,
Artion Kashuri
,
Pshtiwan Mohammed
,
Juan Eduardo Napoles Valdes
Kaynakça
- [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279,
57–66, 2015.
- [2] P. Agarwal, S.S. Dragomir, M. Jleli and B. Samet, Advances in mathematical inequalities and applications, Trends in Mathematics. Birkhäuser/Springer, Singapore,
2018.
- [3] F.M. Atıcı and H. Yaldız, Convex functions on discrete time domains, Canad. Math.
Bull. 59 (2), 225–233, 2016.
- [4] J. Barić, R. Bibi, M. Bohner, A. Nosheen and J. Pečarić, Jensen inequalities on time
scales, volume 9 of Monographs in Inequalities, ELEMENT, Zagreb, 2015.
- [5] J. Barić, R. Bibi, M. Bohner and J. Pečarić, Time scales integral inequalities for
superquadratic functions, J. Korean Math. Soc. 50 (3), 465–477, 2013.
- [6] K.S. Chiu and T. Li, Oscillatory and periodic solutions of differential equations with
piecewise constant generalized mixed arguments, Math. Nachr. 292 (10), 2153–2164,
2019.
- [7] P. Ciatti, M.G. Cowling and F. Ricci, Hardy and uncertainty inequalities on stratified
Lie groups, Adv. Math. 277, 365–387, 2015.
- [8] H. Gunawan and Eridani, Fractional integrals and generalized Olsen inequalities,
Kyungpook Math. J. 49 (1), 31–39, 2009.
- [9] M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl.
80 (2), 545–550, 1981.
- [10] M. Iqbal, M.I. Bhatti and K. Nazeer, Generalization of inequalities analogous to
Hermite-Hadamard inequality via fractional integrals, Bull. Korean Math. Soc. 52
(3), 707–716, 2015.
- [11] H. Kalsoom, M.A. Ali, M. Idrees, P. Agarwal and M. Arif, New post quantum analogues of Hermite-Hadamard type inequalities for interval-valued convex functions,
Math. Probl. Eng. Art. ID 5529650, 17 pages, 2021.
- [12] M.A. Khan, T. Ali, S.S. Dragomir and M.Z. Sarikaya, Hermite-Hadamard type inequalities for conformable fractional integrals, Rev. R. Acad. Cienc. Exactas Fís. Nat.
Ser. A Mat. RACSAM 112 (4),1033–1048, 2018.
- [13] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special
means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (1), 137–
146, 2004.
- [14] T. Li, N. Pintus and G. Viglialoro, Properties of solutions to porous medium problems
with different sources and boundary conditions, Z. Angew. Math. Phys. 70 (3), No.
86, 18, 2019.
- [15] T. Li and G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even
in the attraction-dominated regime, Differential Integral Equations, 34 (5-6), 315–336,
2021.
- [16] K. Mehrez and P. Agarwal, New Hermite-Hadamard type integral inequalities for
convex functions and their applications, J. Comput. Appl. Math. 350, 274–285, 2019.
- [17] P.O. Mohammed, Hermite-Hadamard inequalities for Riemann-Liouville fractional
integrals of a convex function with respect to a monotone function, Math. Methods
Appl. Sci. 44 (3), 2314–2324, 2021.
- [18] P.O. Mohammed and T. Abdeljawad, Modification of certain fractional integral inequalities for convex functions, Adv. Difference Equ. 2020, 69, 2020.
- [19] P.O. Mohammed, T. Abdeljawad, D. Baleanu, A. Kashuri, F. Hamasalh and P. Agarwal, New fractional inequalities of Hermite-Hadamard type involving the incomplete
gamma functions, J. Inequal. Appl. 263, 1–16, 2020.
- [20] P.O. Mohammed and F.K. Hamasalh, New conformable fractional integral inequalities
of Hermite-Hadamard type for convex functions, Symmetry, 11 (2), 2019.
- [21] P.O. Mohammed and M.Z. Sarikaya, Hermite-Hadamard type inequalities for F-convex function involving fractional integrals, J. Inequal. Appl. 359, 1–33, 2018.
- [22] P.O. Mohammed and M.Z. Sarikaya, On generalized fractional integral inequalities
for twice differentiable convex functions, J. Comput. Appl. Math. 372, 112740, 15,
2020.
- [23] P.O. Mohammed, M.Z. Sarikaya and D. Baleanu, On the generalized Hermite-
Hadamard inequalities via the tempered fractional integrals, Symmetry 12 (4), 2020.
- [24] F. Qi, P.O. Mohammed, J.C. Yao and Y.H. Yao, Generalized fractional integral inequalities of Hermite-Hadamard type for $(\alpha,m)$-convex functions, J. Inequal. Appl.
135, 1–17, 2019.
- [25] M. Ruzhansky, Y.J. Cho, P. Agarwal and I. Area, eds, Advances in real and complex
analysis with applications, Trends in Mathematics. Birkhäuser/Springer, Singapore,
2017.
- [26] M.Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-
Liouville fractional integrals, Miskolc Math. Notes, 17 (2), 1049–1059, 2016.
- [27] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical
Library. Cambridge University Press, Cambridge, 1995.
- [28] H. Yaldız and P. Agarwal, s-convex functions on discrete time domains, Analysis, 37
(4), 179–184, 2017.
- [29] X.X. You, M.A. Ali, H. Budak, P. Agarwal and Y.M. Chu, Extensions of Hermite-
Hadamard inequalities for harmonically convex functions via generalized fractional
integrals, J. Inequal. Appl. 102, 1–22, 2021.
Hermite-Hadamard-type inequalities for conformable integrals
Yıl 2022,
Cilt: 51 Sayı: 3, 775 - 786, 01.06.2022
Martin Bohner
,
Artion Kashuri
,
Pshtiwan Mohammed
,
Juan Eduardo Napoles Valdes
Öz
In this study, some inequalities of Hermite-Hadamard type for integrals arising in conformable fractional calculus are presented. In fact, the obtained inequalities are not only valid for those integrals arising in conformable fractional calculus, but for more general integrals as well. Numerous known versions are recovered as special cases. We also illustrate our findings via applications to modified Bessel functions, special means, and midpoint approximations.
Kaynakça
- [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279,
57–66, 2015.
- [2] P. Agarwal, S.S. Dragomir, M. Jleli and B. Samet, Advances in mathematical inequalities and applications, Trends in Mathematics. Birkhäuser/Springer, Singapore,
2018.
- [3] F.M. Atıcı and H. Yaldız, Convex functions on discrete time domains, Canad. Math.
Bull. 59 (2), 225–233, 2016.
- [4] J. Barić, R. Bibi, M. Bohner, A. Nosheen and J. Pečarić, Jensen inequalities on time
scales, volume 9 of Monographs in Inequalities, ELEMENT, Zagreb, 2015.
- [5] J. Barić, R. Bibi, M. Bohner and J. Pečarić, Time scales integral inequalities for
superquadratic functions, J. Korean Math. Soc. 50 (3), 465–477, 2013.
- [6] K.S. Chiu and T. Li, Oscillatory and periodic solutions of differential equations with
piecewise constant generalized mixed arguments, Math. Nachr. 292 (10), 2153–2164,
2019.
- [7] P. Ciatti, M.G. Cowling and F. Ricci, Hardy and uncertainty inequalities on stratified
Lie groups, Adv. Math. 277, 365–387, 2015.
- [8] H. Gunawan and Eridani, Fractional integrals and generalized Olsen inequalities,
Kyungpook Math. J. 49 (1), 31–39, 2009.
- [9] M.A. Hanson, On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl.
80 (2), 545–550, 1981.
- [10] M. Iqbal, M.I. Bhatti and K. Nazeer, Generalization of inequalities analogous to
Hermite-Hadamard inequality via fractional integrals, Bull. Korean Math. Soc. 52
(3), 707–716, 2015.
- [11] H. Kalsoom, M.A. Ali, M. Idrees, P. Agarwal and M. Arif, New post quantum analogues of Hermite-Hadamard type inequalities for interval-valued convex functions,
Math. Probl. Eng. Art. ID 5529650, 17 pages, 2021.
- [12] M.A. Khan, T. Ali, S.S. Dragomir and M.Z. Sarikaya, Hermite-Hadamard type inequalities for conformable fractional integrals, Rev. R. Acad. Cienc. Exactas Fís. Nat.
Ser. A Mat. RACSAM 112 (4),1033–1048, 2018.
- [13] U.S. Kirmaci, Inequalities for differentiable mappings and applications to special
means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (1), 137–
146, 2004.
- [14] T. Li, N. Pintus and G. Viglialoro, Properties of solutions to porous medium problems
with different sources and boundary conditions, Z. Angew. Math. Phys. 70 (3), No.
86, 18, 2019.
- [15] T. Li and G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even
in the attraction-dominated regime, Differential Integral Equations, 34 (5-6), 315–336,
2021.
- [16] K. Mehrez and P. Agarwal, New Hermite-Hadamard type integral inequalities for
convex functions and their applications, J. Comput. Appl. Math. 350, 274–285, 2019.
- [17] P.O. Mohammed, Hermite-Hadamard inequalities for Riemann-Liouville fractional
integrals of a convex function with respect to a monotone function, Math. Methods
Appl. Sci. 44 (3), 2314–2324, 2021.
- [18] P.O. Mohammed and T. Abdeljawad, Modification of certain fractional integral inequalities for convex functions, Adv. Difference Equ. 2020, 69, 2020.
- [19] P.O. Mohammed, T. Abdeljawad, D. Baleanu, A. Kashuri, F. Hamasalh and P. Agarwal, New fractional inequalities of Hermite-Hadamard type involving the incomplete
gamma functions, J. Inequal. Appl. 263, 1–16, 2020.
- [20] P.O. Mohammed and F.K. Hamasalh, New conformable fractional integral inequalities
of Hermite-Hadamard type for convex functions, Symmetry, 11 (2), 2019.
- [21] P.O. Mohammed and M.Z. Sarikaya, Hermite-Hadamard type inequalities for F-convex function involving fractional integrals, J. Inequal. Appl. 359, 1–33, 2018.
- [22] P.O. Mohammed and M.Z. Sarikaya, On generalized fractional integral inequalities
for twice differentiable convex functions, J. Comput. Appl. Math. 372, 112740, 15,
2020.
- [23] P.O. Mohammed, M.Z. Sarikaya and D. Baleanu, On the generalized Hermite-
Hadamard inequalities via the tempered fractional integrals, Symmetry 12 (4), 2020.
- [24] F. Qi, P.O. Mohammed, J.C. Yao and Y.H. Yao, Generalized fractional integral inequalities of Hermite-Hadamard type for $(\alpha,m)$-convex functions, J. Inequal. Appl.
135, 1–17, 2019.
- [25] M. Ruzhansky, Y.J. Cho, P. Agarwal and I. Area, eds, Advances in real and complex
analysis with applications, Trends in Mathematics. Birkhäuser/Springer, Singapore,
2017.
- [26] M.Z. Sarikaya and H. Yildirim, On Hermite-Hadamard type inequalities for Riemann-
Liouville fractional integrals, Miskolc Math. Notes, 17 (2), 1049–1059, 2016.
- [27] G.N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical
Library. Cambridge University Press, Cambridge, 1995.
- [28] H. Yaldız and P. Agarwal, s-convex functions on discrete time domains, Analysis, 37
(4), 179–184, 2017.
- [29] X.X. You, M.A. Ali, H. Budak, P. Agarwal and Y.M. Chu, Extensions of Hermite-
Hadamard inequalities for harmonically convex functions via generalized fractional
integrals, J. Inequal. Appl. 102, 1–22, 2021.