Volume 16, Issue 1 (4-2021)                   IJMSI 2021, 16(1): 195-212 | Back to browse issues page

XML Print

In this paper, we have obtained weighted versions of Ostrowski, Čebysev and Grüss type inequalities for conformable fractional integrals which is given by Katugompola. By using the Katugampola definition for conformable calculus, the present study confirms previous findings and contributes additional evidence that provide the bounds for more general functions.
Type of Study: Research paper | Subject: General

1. T. Abdeljawad, On conformable fractional calculus,textit{Journal of Computational and Applied Mathematics}, textbf{279}, (2015), 57--66. [DOI:10.1016/j.cam.2014.10.016]
2. D. R. Anderson, textit{Taylor's formula and integral inequalities for conformable fractional derivatives}, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer,to appear.
3. A. Atangana, D. Baleanu, and A. Alsaedi, New properties of conformable derivative, textit{Open Math.}, textbf{13}, (2015), 889-898. [DOI:10.1515/math-2015-0081]
4. P. L. v{C}ebyv{s}ev, Sur less expressions approximatives des integrales definies par les autres prises entre les memes limites,textit{Proc. Math. Soc. Charkov }, textbf{2}, (1882), 93-98.
5. R. Gorenflo, F. Mainardi, textit{Fractional calculus:integral and differential equations of fractional order}, Springer Verlag,Wien, 223-276, 1997. [DOI:10.1007/978-3-7091-2664-6_5]
6. G. Gruss, {U}ber das maximum des absoluten Betrages textit{ }$frac{1}{b-a}int limits_{a}^{b}f(x)g(x)dx-frac{1}{(b-a)^{2}}int limits_{a}^{b}f(x)dxint limits_{a}^{b}g(x)dx$, textit{Math. Z.}, textbf{39}, (1935), 215-226. [DOI:10.1007/BF01201355]
7. Abu Hammad, R. Khalil, Abel s formula and wronskian for conformable fractional differential equations, textit{International Journal of Differential Equations and Applications}, textbf{13}(3), (2014), 177-183.
8. O. S. Iyiola and E. R.Nwaeze, Some new results on the new conformable fractional calculus with application using D Alambert approach, textit{Progr. Fract. Differ. Appl.}, textbf{2}(2), (2016), 115-122. [DOI:10.18576/pfda/020204]
9. U. Katugampola, A new fractional derivative with classical properties, ArXiv:1410.6535v2.
10. R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, textit{Journal of Computational Applied Mathematics}, textbf{264}, (2014), 65-70. [DOI:10.1016/j.cam.2014.01.002]
11. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, textit{Theory and Applications of Fractional Differential Equations}, North-Holland Mathematics Studies, 204, Elsevier Sci. B.V., Amsterdam, 2006.
12. S. Miller and B. Ross, textit{An introduction to the Fractional Calculus and Fractional Differential Equations}, John Wiley Sons, USA, 1993.
13. D. S. Mitrinvi'{c}, J. E. Pecari'{c} and A. M. Fink, textit{Classical and New Inequalities in Analysis}, Kluwer Academic Publishers, Dordrecht, 1993. [DOI:10.1007/978-94-017-1043-5]
14. D. S. Mitrinovi{c}, J. E. Pecari{c} and A. M. Fink, textit{Inequalities involving functions and their integrals and derivatives}, Springer Science & Business Media, 2012.
15. A. M. Ostrowski, textit{{U}ber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert}, textit{Comment. Math.Helv.}, textbf{10}, (1938), 226-227. [DOI:10.1007/BF01214290]
16. B.G. Pachpatte, textit{Analytic Inequalities}. Atlantis Press, Paris, 2012. [DOI:10.2991/978-94-91216-44-2]
17. I. Podlubni, textit{Fractional Differential Equations},Academic Press, San Diego, 1999.
18. M. Z. Sarikaya, On the Ostrowski type integral inequality, textit{Acta Math. Univ. Comenianae}, textbf{LXXIX}(1), (2010), 129-134.
19. M. Z. Sarikaya and H. Budak, New inequalities of Opial type for conformable fractional integrals, textit{Turk. J. Math}, textbf{41}(5), (2017), 1164 - 1173. [DOI:10.3906/mat-1606-91]