Several integral inequalities for generalized Riemann-Liouville fractional operators

Yıl 2021, Cilt: 70 Sayı: 1, 269 - 278, 30.06.2021

Juan Gabriel Galeano Delgado Juan Eduardo Napoles Valdes Edgardo Pérez Reyes

https://doi.org/10.31801/cfsuasmas.771172

Cited By: 2

Öz

In this paper, using a generalized integral operator, of the Riemann-Liouville type, defined and studied in a previous work by the authors, we obtain various integral inequalities for positive functions, which contains several reported in the literature. Various remarks carried out throughout the work and pointed out in the Conclusions, show the scope and strength of our results, in particular, it is shown that under particular cases of the considered kernel, several known fractional integral operators are obtained.

Anahtar Kelimeler

Generalized fractional operator, Riemann-Liouville integral, integral inequalities

Kaynakça

• Ahmad, B., Alsaedi, A., Kirane, M., Toberek, B. T., Hermite-Hadamard, Hermite-HadamarFejer, Dragomir-Agarwal and pachpatte tyoe inequalities for convex functions via new fractional integrals, ArXiv: 1701.00092
• DÌaz, R., Pariguan, E., On hypergeometric functions and Pochhammer k-symbol, Divulg. Mat., 15(2) (2007), 179-192.
• Galeano, J., N·poles, J., Perez, E., On a general formulation of the fractional operator Riemann-Liouville and related inequalities, submitted.
• Hadamard, J., Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann, J. Math. Pures Appl., 58 (1893), 171-216.
• Houas, M., Dahmani, Z., Sarikaya, M. Z., Some integral inequalities for (k,s) - Riemann Liouville fractional operators, Journal of Interdisciplinary Mathematics, 23(8) (2020), 1487- 1495, https://doi.org/10.1080/09720502.201
• Katugampola, U. N., New Approach Generalized Fractional Integral, Applied Math and Comp., 218 (2011), 860-865, https://doi.org/10.1016/j.amc.2011.03.062.
• Mubeen, S., Habibullah, G. M., K-fractional integrals and applications, Int. J. Contem. Math. Sci., 7(2) (2012), 89-94.
• 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 FÃ-s. Nat., Ser. A Mat., 111(2) (2017), 425-434, https://doi.org/10.1007/s13398-016-0302-6.
• Rainville, E. D., Special Functions, Macmillan Co., New York, 1960.
• 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(1) (2018), 1-22, https://doi.org/10.7153/jmi-2018-12-01.