A study on error bounds for Newton-type inequalities in conformable fractional integrals

References

[1] Abdeljawad, T.: On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57–66.10.1016/j.cam.2014.10.016Search in Google Scholar

[2] Abdelhakim, A. A.: The flaw in the conformable calculus: It is conformable because it is not fractional, Fract. Calc. Appl. Anal. 22 (2019), 242–254.10.1515/fca-2019-0016Search in Google Scholar

[3] Ali, M. A.—Budak, H.—Fečkan, M.—Patanarapeelert, N.—Sitthiwirattham, T.: On some Newton’s type inequalities for differentiable convex functions via Riemann–Liouville fractional integrals, Filomat 37(11) (2023).10.1186/s13660-023-02953-xSearch in Google Scholar

[4] Ali, M. A.—Budak, H.—Zhang, Z.: A new extension of quantum Simpson’s and quantum Newton’s type inequalities for quantum differentiable convex functions, Math. Methods Appl. Sci. 45(4) (2022), 1845–1863.10.1002/mma.7889Search in Google Scholar

[5] Alomari, M. W.: A companion of Dragomir’s generalization of Ostrowski’s inequality and applications in numerical integration, Ukrainian Math. J. 64 (2012), 435–450.10.1007/s11253-012-0661-xSearch in Google Scholar

[6] Anastassiou, G. A.: Generalized Fractional Calculus: New Advancements and Aplications, Springer, Switzerland, 2021.10.1007/978-3-030-56962-4Search in Google Scholar

[7] Attia, N.—Akgul, A.—Seba, D.—Nour, A.: An efficient numerical technique for a biological population model of fractional order, Chaos Solitons Fractals 141 (2020), Art. ID 110349.10.1016/j.chaos.2020.110349Search in Google Scholar

[8] Awan, M. U.—Talib, S.—Chu, Y. M.—Noor, M. A.—Noor, K. I.: Some new refinements of Hermite–Hadamard-type inequalities involving Riemann–Liouville fractional integrals and applications, Math. Probl. Eng. 2020 (2020), Art. ID 3051920.10.1155/2020/3051920Search in Google Scholar

[9] Erden, S.—Iftikhar, S.—Kumam, P.—Thounthong, P.: On error estimations of Simpson’s second type quadrature formula, Math. Methods Appl. Sci. 2020 (2020), 1–13.10.1002/mma.7019Search in Google Scholar

[10] Erden, S.—Iftikhar, S.—Kumam, P.—Awan, M. U.: Some Newton’s like inequalities with applications, Rev. Acad. Colombiana Cienc. Exact. Fís. Natur. Ser. A Mat. 114(4) (2020), 1–13.10.1007/s13398-020-00926-zSearch in Google Scholar

[11] Gabr, A.—Abdel Kader, A. H.—Abdel Latif, M. S. The Effect of the Parameters of the Generalized Fractional Derivatives On the Behavior of Linear Electrical Circuits, Int. J. Appl. Comput. Math. 7 (2021), Art. No. 247.10.1007/s40819-021-01160-wSearch in Google Scholar

[12] Gao, S.—Shi, W.: On new inequalities of Newton’s type for functions whose second derivatives absolute values are convex, Int. J. Pure Appl. Math. 74(1) (2012), 33–41.Search in Google Scholar

[13] Gorenflo, R.—Mainardi, F.: Fractional calculus: Integral and Differential Equations of Fractional Order, Springer Verlag, Wien, 1997.10.1007/978-3-7091-2664-6_5Search in Google Scholar

[14] Hezenci, F.—Budak, H.—Kosem, P.: A new version of Newton’s inequalities for Riemann-Liouville fractional integrals, Rocky Mountain J. Math. 52(6) (2022).10.1216/rmj.2023.53.1117Search in Google Scholar

[15] Hyder, A.—Soliman, A. H.: A new generalized θ-conformable calculus and its applications in mathematical physics, Phys. Scr. 96 (2020), 015208.10.1088/1402-4896/abc6d9Search in Google Scholar

[16] Iftikhar, S.—Erden, S.—Ali, M. A.—Baili, J.—Ahmad, H.: Simpson’s second-type inequalities for co-ordinated convex functions and applications for cubature formulas, Fractal Fract. 6(1) (2022), Art. No. 33.10.3390/fractalfract6010033Search in Google Scholar

[17] Iftikhar, S.—Kumam, P.—Erden, S.: Newton’s-type integral inequalities via local fractional integrals, Fractals 28(3) (2020), Art. ID 2050037.10.1142/S0218348X20500371Search in Google Scholar

[18] Iftikhar, S.—Erden, S.—Kumam, P.—Awan, M. U.: Local fractional Newton’s inequalities involving generalized harmonic convex functions, Adv. Difference Equ. 2020(1) (2020), 1–14.10.1186/s13662-020-02637-6Search in Google Scholar

[19] Jarad, F.—Abdeljawad, T.—Baleanu, D.: On the generalized fractional derivatives and their Caputo modification, J. Nonlinear Sci. Appl. 10(5) (2017), 2607–2619.10.22436/jnsa.010.05.27Search in Google Scholar

[20] Jarad, F.—Uğurlu, E.—Abdeljawad, T.—Baleanu, D.: On a new class of fractional operators, Adv. Difference Equ. 2017 (2017), Art. No. 247.10.1186/s13662-017-1306-zSearch in Google Scholar

[21] Khalil, R.—Al Horani, M.—Yousef, A.—Sababheh, M.: A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65–70.10.1016/j.cam.2014.01.002Search in Google Scholar

[22] Kilbas, A. A.—Srivastava, H. M.—Trujillo, J. J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, Vol. 204, Elsevier Sci. B. V., Amsterdam, 2006.Search in Google Scholar

[23] Luangboon, W.—Nonlaopon, K.—Tariboon, J.—Ntouyas, S. K.: Simpson- and Newton-type inequalities for convex functions via (p, q)-calculus, Mathematics 9(12) (2021), Art. No. 1338.10.3390/math9121338Search in Google Scholar

[24] Noor, M. A.—Noor, K. I.—Iftikhar, S.: Some Newton’s type inequalities for harmonic convex functions, J. Adv. Math. Stud. 9(1) 2016, 07–16.10.2298/FIL1609435NSearch in Google Scholar

[25] Noor, M. A.—Noor, K. I.—Iftikhar, S.: Newton inequalities for p-harmonic convex functions, Honam Math. J. 40(2) 2018, 239–250.Search in Google Scholar

[26] Pečarić, J. E.—Proschan, F.—Tong, Y. L.: Convex Functions, Partial Orderings and Statistical Applications, Academic Press, Boston, 1992.Search in Google Scholar

[27] Sarikaya, M. Z.—Set, E.—Yaldiz, H.—Basak, N.: Hermite–Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model. Dyn. Syst. 57 (2013), 2403–2407.10.1016/j.mcm.2011.12.048Search in Google Scholar

[28] Sitthiwirattham, T.—Nonlaopon, K.—Ali, M. A.—Budak, H.: Riemann–Liouville fractional Newton’s type inequalities for differentiable convex functions, Fractal Fract. 6(3) (2022), Art. No. 175.10.3390/fractalfract6030175Search in Google Scholar

[29] Uchaikin, V. V.: Fractional Derivatives for Physicists and Engineers, Springer: Berlin/Heidelberg, Germany, 2013.10.1007/978-3-642-33911-0Search in Google Scholar

[30] Zhao, D.—Luo, M.: General conformable fractional derivative and its physical interpretation, Calcolo 54 (2017), 903–917.10.1007/s10092-017-0213-8Search in Google Scholar