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 functionsAbstract
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.
References
P. L. Chebyshev, Sur les expressions approximatives des integrales dnies par les autres prises entre les memes limite, Proc. Math. Soc. Kharkov. 2(1882):93-98.
Z. Dahmani, New Inequalities in Fractional Integrals, International Journal of Nonlinear Science, 9(2010), 493-497.
R. Díaz, E. Pariguan, On hypergeometric functions and Pochhammer k-symbol. Divulg. Mat. 15(2), 179-192 (2007).
Juan D. Galeano, Juan E. Nápoles, Edgardo Pérez, On a general formulation of the fractional operator Riemann-Liouville and related inequalities, submitted.
P. O. Mohammed, Inequalities of (k;s), (k;h)-type for Riemann-Liouville Fractional Integrals, Applied Mathematics E-Notes, 17(2017), 199-206
S. Mubeen, G. M. Habibullah, k-fractional integrals and applications. Int. J. Contemp. Math. Sci. 7, 89-94 (2012).
S. Mubeen, G. M. Habibullah, M. N. Naeem, The Minkowski inequality involving generalized k-fractional conformable integral, J. Inequal. Appl. 2019, 81 (2019). https://doi.org/10.1186/s13660-019-2040-8.
F. Qi, B. N. Guo, Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function. Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 111(2), 425-434 (2017). https://doi.org/10.1007/s13398-016-0302-6.
F. Qi, S. Habib, S. Mubeen, M. N. Naeem, Generalized k-fractional conformable integrals and related inequalities, AIMS Mathematics, 4(3): 343-358 DOI:10.3934/math.2019.3.343.
E. D. Rainville, Special Functions. Macmillan Co., New York (1960).
S. Rashid, Z. Hammouch, H. Kalsoom, R. Ashraf, Y. M. Chu, New Investigation on the Generalized k-Fractional Integral Operators, Frontiers in Physics February 2020 | Volume 8 | Article 25 doi: 10.3389/fphy.2020.00025.
M. Z. Sarikaya, Z. Dahmani, M. E. Kiris, F. Ahmad, (k,s)-Riemann-Liouville fractional integral and applications, Hacettepe Journal of Mathematics and Statistics Volume 45 (1) (2016), 77-89.
Z. H. Yang, J. F. Tian, Monotonicity and inequalities for the gamma function. J. Inequal. Appl. 2017, 317 (2017). https://doi.org/10.1186/s13660-017-1591-9.
Z. H. Yang, J. F. Tian, Monotonicity and sharp inequalities related to gamma function. J. Math. Inequal. 12(1), 1-22 (2018). https://doi.org/10.7153/jmi-2018-12-01.