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

Yıl 2016, Cilt: 4 Sayı: 2, 138 - 146, 01.03.2016

Abdullah Akkurt , M. Esra Yildirim Huseyin Yildirim Yildirim

https://izlik.org/JA43MP64JN

Öz

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.

Anahtar Kelimeler

Riemann-Liouville fractional integral

Kaynakça

• 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.