TY  - JOUR
T1  - A note on conformable fractional Newton-type inequalities via functions of bounded variation
AU  - Hezenci, Fatih
AU  - Sarıışık, Mehmet
AU  - Budak, Hüseyin
PY  - 2025
DA  - November
Y2  - 2025
JF  - Düzce Mathematical Research
PB  - Duzce University
WT  - DergiPark
SN  - 3108-5741
SP  - 11
EP  - 21
VL  - 1
IS  - 1
LA  - en
AB  - In this paper, we establish an equality in order to obtain conformable fractional Newton-type inequalities. Moreover, we prove some Newton-type inequalities associated with conformable fractional operators for functions of bounded variation. Furthermore, some results are presented by using special choices of the obtained inequalities.
KW  - Conformable fractional integrals
KW  - functions of bounded
variations
KW  - Newton-type inequalities
CR  - [1] S. Gao, W. Shi (2012), On new inequalities of Newton’s type for functions whose second derivatives absolute values are convex, Int. J. Pure Appl. Math., 74(1), 33–41.
CR  - [2] S. Erden, S. Iftikhar, P. Kumam, P. Thounthong (2020), On error estimations of Simpson’s second type quadrature formula, Math. Methods Appl. Sci., 47(13), 11232–11244. https://doi.org/10.1002/mma.7019
CR  - [3] M.A. Ali, H. Budak, Z. Zhang (2022), A new extension of quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex functions, Math. Methods Appl. Sci., 45(4), 1845–1863. https://doi.org/10.1002/mma.7889
CR  - [4] M.A. Noor, K.I. Noor, S. Iftikhar (2016), Some Newton’s type inequalities for harmonic convex functions, J. Adv. Math. Stud., 9(1), 07–16.
CR  - [5] M.A. Noor, K.I. Noor, S. Iftikhar (2018), Newton inequalities for p-harmonic convex functions, Honam Math. J., 40(2), 239–250. https://dx.doi.org/10.5831/HMJ.2018.40.2.239
CR  - [6] S. Iftikhar, P. Kumam, S. Erden (2020), Newton’s-type integral inequalities via local fractional integrals, Fractals, 28(03), 2050037. https://doi.org/10.1142/S0218348X20500371
CR  - [7] S. Iftikhar, S. Erden, M.A. Ali, J. Baili, H. Ahmad (2022), Simpson’s second-type inequalities for co-ordinated convex functions and applications for cubature formulas, Fractal Fract., 6(1), 33.
https://doi.org/10.3390/fractalfract6010033
CR  - [8] M.A. Noor, K.I. Noor, M.U. Awan (2015), Some Newton’s type inequalities for geometrically relative convex functions, Malaysian J. Math. Sci., 9(3), 491–502.
CR  - [9] M.Z. Sarıkaya, E. Set, H. Yaldız, N. Başak (2013), Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modelling, 57, 2403–2407. https://doi.org/10.1016/j.mcm.2011.12.048
CR  - [10] R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, Springer Verlag, Wien, 1997.
CR  - [11] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier, Amsterdam, 2006.
CR  - [12] T. Sitthiwirattham, K. Nonlaopon, M.A. Ali, H. Budak (2022), Riemann-Liouville fractional Newton’s type inequalities for differentiable convex functions, Fractal Fract. 6(3), 175. https://doi.org/10.3390/fractalfract6030175
CR  - [13] S. Erden, S. Iftikhar, P. Kumam, M.U. Awan (2020), Some Newton’s like inequalities with applications, RACSAM Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Mat., 114(4), 1–13. https://doi.org/10.1007/s13398-020-00926-z
CR  - [14] F. Hezenci, H. Budak (2025), Fractional Newton-type integral inequalities by means of various function classes, Math. Methods Appl. Sci., 48(1), 1198–1215. https://doi.org/10.1002/mma.10378
CR  - [15] S. Iftikhar, S. Erden, P. Kumam, M.U. Awan (2020), Local fractional Newton’s inequalities involving generalized harmonic convex functions, Adv. Difference Equ., 2020(1), 1–14. https://doi.org/10.1186/s13662-020-02637-6
CR  - [16] F. Hezenci, H. Budak, P. Kösem (2023), A new version of Newton’s inequalities for Riemann-Liouville fractional integrals, Rocky Mountain J. Math., 53(1), 49–64. https://doi.org/10.1216/rmj.2023.53.49
CR  - [17] F. Hezenci, H. Budak (2023), Some perturbed Newton type inequalities for Riemann-Liouville fractional integrals, Rocky Mountain J. Math., 53(4), 1117–1127. https://doi.org/10.1216/rmj.2023.53.1117
CR  - [18] V.V. Uchaikin, Fractional derivatives for physicists and engineers, Springer: Berlin/Heidelberg, Germany, 2013.
CR  - [19] G.A. Anastassiou, Generalized fractional calculus: New advancements and applications, Springer: Switzerland, 2021.
CR  - [20] N. Attia, A. Akgül, D. Seba, A. Nour (2020), An efficient numerical technique for a biological population model of fractional order, Chaos, Solitons & Fractals, 141, 110349.
https://doi.org/10.1016/j.chaos.2020.110349
CR  - [21] A. Gabr, A.H. Abdel Kader, M.S. Abdel Latif (2021), The effect of the parameters of the generalized fractional derivatives on the behavior of linear electrical circuits, Int. J. Appl. Comput. Math., 7, 247. https://doi.org/10.1007/s40819-021-01160-w
CR  - [22] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh (2014), A new definition of fractional derivative, J. Comput. Appl. Math., 264, 65–70. https://doi.org/10.1016/j.cam.2014.01.002
CR  - [23] A.A. Abdelhakim (2019), The flaw in the conformable calculus: It is conformable because it is not fractional, Fract. Calc. Appl. Anal., 22, 242–254. https://doi.org/10.1515/fca-2019-0016
CR  - [24] D. Zhao, M. Luo (2017), General conformable fractional derivative and its physical interpretation, Calcolo, 54, 903–917. https://doi.org/10.1007/s10092-017-0213-8
CR  - [25] A. Hyder, A.H. Soliman (2020), A new generalized q-conformable calculus and its applications in mathematical physics, Phys. Scr., 96, 015208. https://doi.org/10.1088/1402-4896/abc6d9
CR  - [26] F. Jarad, E. Uğurlu, T. Abdeljawad, D. Baleanu (2017), On a new class of fractional operators, Adv. Difference Equ., 2017, 247. https://doi.org/10.1186/s13662-017-1306-z
CR  - [27] T. Abdeljawad (2015), On conformable fractional calculus, J. Comput. Appl. Math., 279, 57–66. https://doi.org/10.1016/j.cam.2014.10.016
CR  - [28] H. Budak, C. Ünal, F. Hezenci (2024), A study on error bounds for Newton-type inequalities in conformable fractional integrals, Math. Slovaca, 74(2), 313–330. https://doi.org/10.1515/ms-2024-0024
CR  - [29] F. Hezenci, P. Karagözoglu, H. Budak, Some error bounds for Newton formula in conformable fractional operators, submitted.
CR  - [30] M.W. Alomari (2012), A companion of Dragomir’s generalization of Ostrowski’s inequality and applications in numerical integration, Ukrainian Math. J., 64, 435–450.
UR  - https://dergipark.org.tr/en/pub/dmr/issue//1752712
L1  - https://dergipark.org.tr/en/download/article-file/5098414
ER  -