Dragomir-Agarwal type of inequalities involving fractional integrals of Atangana-Baleanu and generalized M-convex function
*Ibrahim SlimaneCorresponding authorslimaneibrahim@outlook.frFaculty of Exact Sciences and InformaticsAbdelhamid Ibn Badis UniversityMostaganem, P. O. Box 227, 27000, AlgeriaView full profile → , Muhammad Uzair Awanawan.uzair@gmail.comDepartment of MathematicsGC University FaisalabadFaisalabad, PakistanView full profile → , Zarnab Aslamzarnabaslam98@gmail.comDepartment of MathematicsGC University FaisalabadFaisalabad, PakistanView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2023
- Published Online:
- 15 May 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1995
- Pages:
- 1–27
Abstract
Keywords
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References
[1] T. Abdeljawad and D. Baleanu, “Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel,” J. Nonlinear Sci. Appl., vol. 10, pp. 1098–1107 (2017).
[2] A. Atangana and D. Baleanu, “New fractional derivatives with non-local and nonsingular kernel: Theory and application to heat transfer model,” Therm. Sci., vol. 20, no. 2, pp. 763–769 (2016).
[3] M. Alomari, M. Darus, and S. S. Dragomir, “New inequalities of Hermite–Hadamard type for functions whose second derivatives absolute value are quasi-convex,” RGMIA Res. Rep. Collect., vol. 12, Art. 17.
[4] M. U. Awan, M. A. Noor, T. Du, and K. I. Noor, “OnM-convex function,” AIMS Math., vol. 5, no. 3, pp. 2376–2387 (2020).
[5] S. Belarbi and Z. Dahmani, “On some new fractional integral inequalities,” J. Inequal. Pure Appl. Math., vol. 10, no. 3, Art. 86, pp. 1–12 (2009).
[6] H. Budak, M. A. Ali, N. Alp, and H. M. Awais, “Some new q-Hermite-Hadamard type inequalities for the product of convex functions,” J. Interdiscip. Math., vol. 25, no. 8, pp. 2141–2166, 2022.2.
[7] M. Caputo and M. Fabrizio, “A new definition of fractional derivative without singular kernel,” Prog. Fract. Differ. Appl., vol. 1, no. 2, pp. 73–85 (2015).
[8] G. Cristescu and L. Lupsa, Non-connected Convexities and Applications. Dordrecht, The Netherlands: Kluwer Academic (2002).
[9] S. S. Dragomir, “Inequalities of Hermite–Hadamard type for h-convex functions on linear spaces,” Proyecciones, vol. 34, no. 4, pp. 323–341 (2015).
[10] S. S. Dragomir and R. P. Agarwal, “Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula,” Appl. Math. Lett., vol. 11, no. 5, pp. 91–95 (1998).
[11] S. S. Dragomir and B. Mond, “Integral inequalities of Hadamard’s type for logconvex functions,” Demonstr. Math., vol. 2, pp. 354–364 (1998).
[12] S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite–Hadamard Inequality and Applications. Melbourne, Australia: Victoria Univ. (2000).
[13] Gulalai, S. Ahmad, F. A. Rihan, A. Ullah, Q. M. Al-Mdallal, and A. Akgül, “Nonlinear analysis of a nonlinear modified KdV equation under Atangana–Baleanu Caputo,” AIMS Math., vol. 7, no. 5, pp. 7847–7865 (2022).
[14] M. Gürbüz, A. O. Akdemir, and S. Rashid, “Hermite–Hadamard inequality for fractional integrals of Caputo–Fabrizio type and related inequalities,” J. Inequal. Appl., vol. 2020, Art. 172 (2020).
[15] D. A. Ion, “Some estimates on the Hermite–Hadamard inequality through quasiconvex functions,” An. Univ. Craiova Math. Comput. Sci. Ser., vol. 34, pp. 82–87 (2007).
[16] M. Khaled and P. Agarwal, “New Hermite–Hadamard type integral inequalities for convex functions and their applications,” J. Comput. Appl. Math., vol. 350, pp. 274–285 (2019).
[17] M. A. Khan, Y. Khurshid, T.-S. Du, and Y.-M. Chu, “Generalization of Hermite–Hadamard type inequalities via conformable fractional integrals,” J. Funct. Spaces, vol. 2018, Art. ID 5357463 (2018).
[18] A. A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations. Amsterdam, The Netherlands: Elsevier (2006).
[19] M. A. Noor, K. I. Noor, M. U. Awan, and S. Khan, “Fractional Hermite–Hadamard inequalities for some new classes of Godunova–Levin functions,” Appl. Math. Inf. Sci., vol. 8, no. 6, pp. 2865–2872 (2014).
[20] M. E. Özdemir, “On Iyengar-type inequalities via quasi-convexity and quasiconcavity,” Miskolc Math. Notes, vol. 15, no. 1, pp. 171–181 (2014).
[21] F. Rahman, A. Ali, and S. Saifullah, “Analysis of time-fractional ϕ4-equation with singular and non-singular kernels,” Int. J. Appl. Comput. Math., vol. 7, Art. 192 (2021).
[22] M. Z. Sarikaya, E. Set, H. Yaldiz, et al., “Hermite–Hadamard inequalities for fractional integrals and related fractional inequalities,” Math. Comput. Model., vol. 57, pp. 2403–2407 (2013).
[23] S. Saifullah, A. Ali, M. Irfan, and K. Shah, “Time-fractional Klein–Gordon equation with solitary/shock wave solutions,” Math. Probl. Eng., vol. 2021, Art. ID (2021).
[24] E. Set, S. I. Butt, A. O. Akdemir, A. Karaoglan, and T. Abdeljawad, “New integral inequalities for differentiable convex functions via Atangana–Baleanu fractional integral operators,” Chaos Solitons Fractals, vol. 143, Art. 110554 (2021).
[25] E. Set, J. Choi, and B. Celik, “Certain Hermite–Hadamard type inequalities involving generalized fractional integral operators,” Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat., vol. 112, no. 4, pp. 1539–1547 (2018).
[26] I. Slimane and Z. Dahmani, “A continuous and fractional derivative dependence of random differential equations with nonlocal conditions,” J. Interdiscip. Math., vol. 24, no. 6, pp. 1457–1470 (2021).
[27] S. Varosanec, “On h-convexity,” J. Math. Anal. Appl., vol. 326, pp. 303–311 (2007).
[28] B. Y. Xi, S.-P. Bai, and F. Qi, “On integral inequalities of the Hermite–Hadamard type for coordinated (α,m1)–(s,m2)-convex functions,” J. Interdiscip. Math., vol. 21, no. 7–8, pp. 1505–1518 (2018).
[29] Y. Sabir, M. Misiran, and Z. Omar, “Hermite–Hadamard inequality for product of (h1, h2, s)-convex andm-harmonically convex function,” J. Interdiscip. Math., vol. 26, no. 4, pp. 675–689 (2023).
[30] Y. Sabir, Z. Omar, and M. Misiran, “Hermite–Hadamard and Simpson’s type inequalities for first and second ordered derivatives using product of (h1, h2, s)-convex and m-convex function,” J. Interdiscip. Math., vol. 26, no. 8, pp. 1733–1744 (2023).
[31] Y. Zhang, T. S. Du, and H. Wang, “Some new k-fractional integral inequalities containing multiple parameters via generalized (s,m)-preinvexity,” Italian J. Pure Appl. Math., vol. 40, pp. 510–527, 2018.
