Hermite-Hadamard's inequalities for conformable fractional integrals
DOI:
https://doi.org/10.11121/ijocta.01.2019.00559Keywords:
Hölder's inequality, fractional derivative, factional integral, Confromable fractional integrals, trapezoid inequality, midpoint inequality.Abstract
In this paper, we establish the Hermite-Hadamard type inequalities for
conformable fractional integral and we will investigate some integral
inequalities connected with the left and right-hand side of the
Hermite-Hadamard type inequalities for conformable fractional integral. The
results presented here would provide generalizations of those given in
earlier works and we show that some of our results are better than the other
results with respect to midpoint inequalities.
Downloads
References
Beckenbach, E. F. (1948). Convex functions, Bull. Amer. Math. Soc., 54 439-460. http://dx.doi.org/10.1090/s0002-9904-1948-08994-7.
Hermite, C. (1883). Sur deux limites d'une integrale definie, Mathesis, 3, 82.
Farissi, A.E. (2010). Simple Proof and Refinement of Hermite-Hadamard Inequality, J. Math.Inequal, 4(3), 365-369.
Sarikaya, M.Z., Set, E., Yaldız, H. and Başak, N. (2013). Hermite--Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput.Modell. 57 (9), 2403--2407.
Sarikaya, M.Z. and Aktan, N. (2011). On the generalization of some integral inequalities and their applications, Mathematical and Computer Modelling, Volume 54, Issues 9--10, Pages 2175--2182.
U.S. Kırmacı, U.S. (2004). Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comput. 147 (1), 137--146.
Dragomir, S.S. and Agarwal, R.P. (1998). Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Applied Mathematics Letters, 11 (5), 91-95.
Mitrinovic, D.S. (1970). Analytic inequalities. Springer, Berlin-Heidelberg-New York.
Abdeljawad, T. (2015). On conformable fractional calculus, Journal of Computational and Applied Mathematics 279, 57--66.
Anderson D.R. (2016). Taylor’s Formula and Integral Inequalities for Conformable Fractional Derivatives. In: Pardalos P., Rassias T. (eds) Contributions in Mathematics and Engineering. Springer, Cham, pp 25-43 https://doi.org/10.1007/978-3-319-31317-7-2.
Khalil, R., Al horani, M., Yousef, A. and Sababheh, M. (2014). A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264, 65-70.
Iyiola, O.S. and Nwaeze, E.R. (2016). Some new results on the new conformable fractional calculus with application using D'Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122.
Abu Hammad, M. and Khalil, R. (2014). Conformable fractional heat differential equations, International Journal of Differential Equations and Applications 13( 3), 177-183.
Abu Hammad, M. and Khalil, R. (2014). Abel's formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications 13( 3), 177-183.
Akkurt, A., Yıldırım, M.E. and Yıldırım, H. (2017). On Some Integral Inequalities for Conformable Fractional Integrals, Asian Journal of Mathematics and Computer Research, 15(3): 205-212.
Akkurt, A., Yıldırım, M.E. and Yıldırım, H. (2017). A new Generalized fractional derivative and integral, Konuralp Journal of Mathematics, Volume 5 No. 2 pp. 248-259.
Budak, H., Usta, F., Sarikaya, M.Z. and Ozdemir, M.E. (2018). On generalization of midpoint type inequalities with generalized fractional integral operators, Revista de la Real Academia de Ciencias Exactas, F´ısicas y Naturales. Serie A. Matem´aticas, https://doi.org/10.1007/s13398-018-0514-z
Usta, F., Budak, H., Sarikaya, M.Z. and Set, E. (2018). On generalization of trapezoid type inequalities for s-convex functions with generalized fractional integral operators, Filomat, 32(6).
Downloads
Published
How to Cite
Issue
Section
License
Articles published in IJOCTA are made freely available online immediately upon publication, without subscription barriers to access. All articles published in this journal are licensed under the Creative Commons Attribution 4.0 International License (click here to read the full-text legal code). This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your work will ensure your right to make your work freely and openly available.
Under the Creative Commons Attribution 4.0 International License, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, and/or copy articles in IJOCTA, so long as the original authors and source are credited.
The readers are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- for any purpose, even commercially.
- The licensor cannot revoke these freedoms as long as you follow the license terms.
under the following terms:
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
This work is licensed under a Creative Commons Attribution 4.0 International License.