Generalizations of some weighted Opial-type inequalities in conformable calculus
Volume 30, Issue 1, pp 30--37
https://doi.org/10.22436/jmcs.030.01.04
Publication Date: November 25, 2022
Submission Date: July 05, 2022
Revision Date: September 06, 2022
Accteptance Date: September 09, 2022
Authors
S. H. Saker
- Department of Mathematics, Faculty of Science, Mansoura University, Mansoura , Egypt.
G. M. Ashry
- Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt.
M. R. Kenawy
- Department of Mathematics, Faculty of Science, Fayoum University, Fayoum, Egypt.
Abstract
In this paper, we prove new \(\alpha\)-fractional inequalities of Opial type using conformable calculus. From our results we obtain classical integral
inequalities as special cases.
Share and Cite
ISRP Style
S. H. Saker, G. M. Ashry, M. R. Kenawy, Generalizations of some weighted Opial-type inequalities in conformable calculus, Journal of Mathematics and Computer Science, 30 (2023), no. 1, 30--37
AMA Style
Saker S. H., Ashry G. M., Kenawy M. R., Generalizations of some weighted Opial-type inequalities in conformable calculus. J Math Comput SCI-JM. (2023); 30(1):30--37
Chicago/Turabian Style
Saker, S. H., Ashry, G. M., Kenawy, M. R.. "Generalizations of some weighted Opial-type inequalities in conformable calculus." Journal of Mathematics and Computer Science, 30, no. 1 (2023): 30--37
Keywords
- Opial type inequalities
- conformable fractional calculus
- Holder inequalities
- chain rule
MSC
References
-
[1]
T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279 (2015), 57–66
-
[2]
T. Abdeljawad, P. O. Mohammed, A. Kashuri, New modified conformable fractional integral inequalities of Hermite- Hadamard type with applications, J. Funct. Spaces, 2020 (2020), 14 pages
-
[3]
R. P. Agarwal, P. Y. H. Pang, Opial inequalities with applications in differential and difference equations, Kluwer Academic Publishers, Dordrecht (1995)
-
[4]
D. R. Anderson, Taylor’s formula and integral inequalities for conformable fractional derivatives, Contrib. Math. Eng. Springer. Cham., 2016 (), 25–43
-
[5]
P. R. Beesack, On an integral inequality of Z. Opial, Trans. Amer. Math. Soc., 104 (1962), 470–475
-
[6]
P. R. Beesack, K. M. Das, Extensions of Opial’s inequality, Pacific J. Math., 26 (1968), 215–232
-
[7]
M. Bohner, T. S. Hassan, T. Li, Fite-Hille-Wintner-type oscillation criteria for second-order half-linear dynamic equations with deviating arguments, Indag. Math. (N.S.), 29 (2018), 548–560
-
[8]
D. W. Boyd, J. S. W. Wong, An extension of Opial’s inequality, J. Math. Anal. Appl., 19 (1967), 100–102
-
[9]
K.-S. Chiu, T. Li, Oscillatory and periodic solutions of differential equations with piecewise constant generalized mixed arguments, Math. Nachr., 292 (2019), 2153–2164
-
[10]
J. Dˇzurina, S. R. Grace, I. Jadlovsk´a, T. Li, Oscillation criteria for second-order Emden-Fowler delay differential equations with a sublinear neutral term, Math. Nachr., 293 (2020), 910–922
-
[11]
S. Frassu, T. Li, G. Viglialoro, Improvements and generalizations of results concerning attractionrepulsion chemotaxis models, Math. Methods Appl. Sci., 45 (2021), 11067–11078
-
[12]
S. Frassu, G. Viglialoro, Boundedness criteria for a class of indirect (and direct) chemotaxis-consumption models in high dimensions, Appl. Math. Lett., 132 (2022), 7 pages
-
[13]
L.-G. Hua, On an inequality of Opial, Sci. Sinica, 14 (1965), 789–790
-
[14]
R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65–70
-
[15]
M. A. Khan, Y.-M. Chu, A. Kashuri, R. Liko, G. Ali, Conformable fractional integrals versions of Hermite-Hadamard inequalities and their generalizations, J. Funct. Spaces, 2018 (2018), 9 pages
-
[16]
Y. Khurshid, M. A. Khan, Y.-M. Chu, Conformable fractional integral inequalities for GG-and GA-convex function, AIMS Math., 5 (2020), 5012–5030
-
[17]
T. Li, N. Pintus, G. Viglialoro, Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys., 70 (2019), 1–18
-
[18]
T. Li, Y. V. Rogovchenko, Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations, Monatsh. Math., 184 (2017), 489–500
-
[19]
T. Li, Y. V. Rogovchenko, On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett., 105 (2020), 1–7
-
[20]
T. Li, G. Viglialoro, Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differ. Integral Equ., 34 (2021), 315–336
-
[21]
K. S. Nisar, G. Rahman, K. Mehrez, Chebyshev type inequalities via generalized fractional conformable integrals, J. Inequal. Appl., 2019 (2019), 1–9
-
[22]
C. Olech, A simple proof of a certain result of Z. Opial, Ann. Polon. Math., 8 (1960), 61–63
-
[23]
Z. Opial, Sur une in´egalit´, Ann. Polon. Math., 8 (1960), 29–32
-
[24]
S. H. Saker, D. O’ Regan, M. R. Kenawy, R. P. Agarwal, Fractional Hardy Type Inequalities via Conformable Calculus, Mem. Differ. Equ. Math. Phys., 73 (2018), 131–140
-
[25]
M. Z. Sarikaya, H. Yaldiz, H. Budak, On weighted Iyengar-type inequalities for conformable fractional integrals, Math. Sci., 11 (2017), 327–331
-
[26]
E. Set, A. O. Akdemir, ˙I. Mumcu, Chebyshev type inequalities for conformable fractional integrals, Miskolc Math. Notes, 20 (2019), 1227–1236
-
[27]
G.-S. Yang, On a certain result of Z. Opial, Proc. Japan Acad., 42 (1966), 78–83
-
[28]
G.-S. Yang, A note on some integrodifferential inequalities, Soochow J. Math., 9 (1983), 231–236