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In this paper, we present new inequalities of the Hermite–Hadamard type for generalized ϕ-convex functions, within the framework of non-conformable fractional integrals.
Czasopismo
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Tom
Strony
5--16
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
- School of Mathematical Sciences Nanjing Normal University, Nanjing, 210023, China
autor
- Universidad Nacional del Nordeste Facultad de Ciencias Exactas y Naturales y Agrimensura, Corrientes 3400, Argentina
- Universidad Tecnologica Nacional Facultad Regional Resistencia, Resistencia, Chaco 3500, Argentina
autor
- Department of Mathematics Faculty of Technical Science University "Ismail Qemali”, Vlora, Albania
autor
- School of Mathematical Sciences Nanjing Normal University, Nanjing, 210023, China
Bibliografia
- [1] Baleanu D., Fernandez A., On fractional operators and their classifications, Mathematics, 7(830)(2019).
- [2] Dragomir S.S., Pearce C.E.M., Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University, 2000.
- [3] Erdelyi A., Magnus F.W., Oberhettinger, Tricomi F.G., Higher transcendental functions, New York, McGraw-Hill, 3(1955).
- [4] Guzman P.M., Langton G., Lugo L.M., Medina J., Valdes J.E.N., A new definition of a fractional derivative of local type, J. Mat h. Anal., 9(2)(2018), 88-98.
- [5] Hadamard J., Etude sur les proprietes des fonctions entieres et en particulier da une fonction consideree par Riemann, Journ. de Math. (4), 58(1893), 171-215.
- [6] Huang C.-J., Rahman G., Nisar K.S., Ghaffar A., Qi F., Some inequalities of the Hermite–Hadamard type for k-fractional conformable integrals, Aust. J. Math. Anal. Appl., 16(1)(2019), Art. 7, pp. 9.
- [7] Khan M. Adil, Chu Y.-M., Kashuri A., Liko R., Ali G., Conformable fractional integrals versions of Hermite-Hadamard inequalities and their generalizations, J. Function Spaces, 2018(2018), Art. ID 6928130, pp. 9.
- [8] Mohammed P.O., Hamasalh F.K., New conformable fractional integral inequalities of Hermite-Hadamard type for convex functions, Symmetry, 11(263)(2019).
- [9] Mittag-Leffler G.M., Sur la nouvelle fonction, C. R. Acad. Sci., Paris, 137(1903), 554-558.
- [10] Mittag-Leffler G.M., Sur la reprasentation analytique dˆa une branche uniforme d’une fonction monogane, Acta Math., Paris, 29(1904), 101-181.
- [11] Ortigueira M., Martynyuk V., Fedula M., Machado J.A.T., The failure of certain fractional calculus operators in two physical models, Fract. Calc. Appl. Anal., 22(2)(2019).
- [12] Valdes J.E.N., Guzman P.M., Lugo L.M., Some new results on non conformable fractional calculus, Adv. Dyn. Syst. Appl., 13(29)(2018), 167-175.
- [13] Qi F., Habib S., Mubeen S., Naeem M.N., Generalized k-fractional conformable integrals and related inequalities, AIMS Mathematics, 4(3)(2019), 343-358.
- [14] Sarikaya M.Z., Set E., Yaldiz H., Bas¸ak N., Hermite-Hadamard’s inequalities for fractional integrals and related fractional inequalities, Math. Comput. Modelling, 57(2013), 2403–2407.
- [15] Sarikaya M.Z., Yildirim H., On Hermite-Hadamard type inequalities for Riemann-Liouville fractional integrals, Miskolc Math. Notes, 17(2)(2017), 1049–1059.
- [16] Wiman A., Über den fundamentalsatz in der teorie der funktionen Eα(z), Acta Math., 29(1905), 191–201.
- [17] Wang J.-R., Li X., Feckan M., Zhou Y., Hermite–Hadamard-type in equalities for Riemann-Liouville fractional integrals via two kinds of convexity, Appl. Anal., (2012), 1-13.
- [18] Zhu C., Feckan M., Wang J.-R., Fractional integral inequalities for differentiable convex mappings and applications to special means and a midpoint formula, J. Appl. Math. Stat. Inform., 8(2)(2012), 21-28.
Uwagi
EN
This work is partially supported by National Natural Science Foundation of China (No. 11971241).
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Bibliografia
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