New Integral Inequalities Involving Generalized Riemann-Liouville Fractional Operators
DOI:
https://doi.org/10.24193/subbmath.2023.3.02Keywords:
Generalized fractional Riemann-Liouville integral, fractional integral inequality, synchronous functions.Abstract
In this paper, using a generalized operator of the Riemann-Liouville type, defined and studied in a previous work, several integral inequalities for synchronous functions are established.
Mathematics Subject Classification (2010): 26A33, 26D10, 47A63.
References
Abdeljawad, T., Mohammed, P.O., Kashuri, A., New modified conformable fractional integral inequalities of Hermite-Hadamard type with applications, J. Funct. Space., (2020), Article ID 4352357, 14 pages.
Baleanu, D., Mohammed, P.O., Vivas-Cortez, M., et al., Some modifications in con- formable fractional integral inequalities, Adv. Differ. Equ., 2020(2020), 374.
Chebyshev, P.L., Sur les expressions approximatives des intégrales définies par les autres prises entre les mêmes limite, Proc. Math. Soc. Kharkov, 2(1882), 93-98.
Dahmani, Z., New Inequalities in Fractional Integrals, International Journal of Nonlinear Science, 9(2010), 493-497.
Díaz, R., Pariguan, E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15(2007), no. 2, 179-192.
Fernandez, A., Mohammed, P., Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels, Math. Meth. Appl. Sci., (2020), 1-18, https://doi.org/10.1002/mma.6188.
Galeano, J.D., Nápoles, J.E., Pérez, E., On a general formulation of the fractional operator Riemann-Liouville and related inequalities, (submitted).
Guzman, P.M., Karus, P., Nápoles Valdes, J.E., Generalized integral inequalities of Chebyshev type, Fractal Fract., (2020), no. 4, 10, https://doi.org/10.3390/fractalfract4020010.
Mohammed, P.O., Inequalities of (k; s), (k; h)-type for Riemann-Liouville fractional integrals, Applied Mathematics E-Notes, 17(2017), 199-206.
Mohammed, P.O., Abdeljawad, T., Opial integral inequalities for generalized fractional operators with nonsingular kernel, J. Inequal. Appl., 2020(2020), 148.
Mohammed, P.O., Abdeljawad, T., Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel, Adv. Differ. Equ., 2020(2020), 363.
Mohammed, P.O., Brevik, I., A new version of the Hermite-Hadamard in- equality for Riemann-Liouville fractional integrals, Symmetry, 12(2020), 610, https://doi.org/10.3390/sym12040610.
Mohammed, P.O., Sarikaya, M.Z., On generalized fractional integral inequalities for twice differentiable convex functions, J. Comput. Appl. Math., 372(2020), 112740.
Mubeen, S., Habibullah, G.M., k-fractional integrals and applications, Int. J. Contemp. Math. Sci., 7(2012), 89-94.
Mubeen, S., Habibullah, G.M., Naeem, M.N., The Minkowski inequality in- volving generalized k-fractional conformable integral, J. Inequal. Appl., 81(2019), https://doi.org/10.1186/s13660-019-2040-8.
Nápoles Valdes, J.E., Rodriguez, J.M., Sigarreta, J.M., New Hermite-Hadamard type inequalities involving non-conformable integral operators, Symmetry, (2019), 11, 1108, https://doi.org/10.3390/sym11091108.
Qi, F., Guo, B.N., Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function, Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., 111(2017), no. 2, 425-434, https://doi.org/10.1007/s13398-016-0302-6.
Qi, F., Habib, S., Mubeen, S., Naeem, M.N., Generalized k-fractional con- formable integrals and related inequalities, AIMS Mathematics, 4(3)(2019), 343-358, https://doi.org/10.3934/math.2019.3.343.
Rainville, E.D., Special Functions, Macmillan Co., New York, 1960.
Rashid, S., Hammouch, Z., Kalsoom, H., Ashraf, R., Chu, Y.M., New investigation on the generalized k-fractional integral operators, Frontiers in Physics, 8(2020), Article 25, https://doi.org/10.3389/fphy.2020.00025.
Sarikaya, M.Z., Dahmani, Z., Kiris, M.E., Ahmad, F., (k, s)-Riemann-Liouville fractional integral and applications, Hacettepe Journal of Mathematics and Statistics, 45(2016), no. 1, 77-89.
Yang, Z.H., Tian, J.F., Monotonicity and inequalities for the gamma function, J. Inequal. Appl., 317(2017), https://doi.org/10.1186/s13660-017-1591-9.
Yang, Z.H., Tian, J.F., Monotonicity and sharp inequalities related to gamma function, J. Math. Inequal., 12(2018), no. 1, 1-22, https://doi.org/10.7153/jmi-2018-12-01.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
