On some integral inequalities for (k,h)−Riemann-Liouville fractional integral

Year 2016, Volume: 4 Issue: 2, 138 - 146, 01.03.2016

Abdullah Akkurt , M. Esra Yildirim Huseyin Yildirim Yildirim

Abstract

In this study, giving the definition of fractional integral, which are with the help of synchronous and monotonic function,  some fractional integral inequalities have established.

Keywords

Riemann-Liouville fractional integral

References

• Anastassiou GA, Hooshmandasl MR, Ghasemi A, Moftakharzadeh F. Montgomery identities for fractional integrals and related fractional inequalities, J. Inequal. Pure Appl. Math., 10(4)(2009), 1-6.
• Anastassiou GA. Fractional Differentiation Inequalities, Springer Science, LLC, 2009.
• Belarbi S, Dahmani Z. On some new fractional integral inequalities, J. Inequal. Pure Appl. Math., 10(3)(2009), 1-12.
• Dahmani Z. New inequalities in fractional integrals, International Journal of Nonlinear Sciences, 9(4)(2010), 493-497.
• Dahmani Z. On Minkowski and Hermite-Hadamad integral inequalities via fractional integration, Ann. Funct. Anal., 1(1)(2010, 51-58.
• Dragomir SS. A generalization of Gruss’s inequality in inner product spaces and applications, J.Math. Annal. Appl., 237(1)(1999), 74-82.
• Mitrinovic DS, Pecaric JE, Fink AM. Classical and New Inequalities in Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
• Pachpatte BG. On multidimensional Gruss type integral inequalities, J. Inequal. Pure Appl. Math., 32 (2002), 1-15. Qi F, Li AJ, Zhao WZ, Niu DW, Cao J. Extensions of several integral inequalities, J. Inequal. Pure Appl. Math., 7(3)(2006), 1-6.
• Qi F. Several integral inequalities, J. Inequal. Pure Appl. Math., 1(2)(2000), 1-9.
• Sarikaya MZ, Aktan N, Yildirim H. On weighted Chebyshev-Gruss like inequalities on time scales, J. Math. Inequal., 2(2)(2008), 185-195.
• Samko SG, Kilbas AA, Marichev OI. Fractional Integrals and Derivatives - Theory and Applications, Gordon and Breach, Linghorne, 1993.
• Akkurt A, Kac¸ar Z, Yildirim H. Generalized Fractional Integrals Inequalities for Continuous Random Variables, Journal of Probability Statistics, Volume 2015, http://dx.doi.org/10.1155/2015/958980, (2015).
• Diaz, R. and Pariguan, E., On hypergeometric functions and Pochhammer k−symbol, Divulg.Math, 15.(2007),179-192.
• P. L. Butzer, A. A. Kilbas and J.J. Trujillo, Fractional calculus in theMellin setting and Hadamard-type fractional integrals, Journal of Mathematical Analysis and Applications, 269, (2002), 1-27.
• U.N. Katugampola, New Approach to a Generalized Fractional Fntegral, Appl. Math. Comput. 218(3), (2011), 860-865.
• A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Diferential Equations, Elsevier B.V., Amsterdam, Netherlands, 2006.
• Akkurt, A., & Yıldırım, H. (2014). Genellestirilmis¸ Fractional Integraller Icin Feng Qi Tipli Integral Esitsizlikleri Uzerine. Fen Bilimleri Dergisi, 1(2).
• Mubeen, S. and Habibullah, G.M., k−fractional integrals and application, Int. J. Contemp. Math. Sciences, 7(2), 2012, 89-94.
• M.Z. Sarikaya, Z. Dahmani, M.E. Kiris and F. Ahmad, (ks)−Riemann-Liouville fractional integral and applications, Hacettepe Journal of Mathematics and Statistics, Accepted.