Abstract
In this paper, we obtain generalized Ostrowski type integral inequalities involving moments of a continuous random variables via local fractional integrals.
Similar content being viewed by others
References
Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach, Yverdon et alibi (1993)
Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
Chen, G.-S.: Generalizations of Hölder’s and some related integral inequalities on fractal space. J. Funct. Spaces Appl. 2013, Article ID 198405 (2013)
Kumar, P.: The Ostrowski type moment integral inequalities and moment-bounds for continuous random variables. Comput. Math. Appl. 49(11–12), 1929–1940 (2005)
Mo, H., Sui, X., Yu, D.: Generalized convex functions on fractal sets and two related inequalities. Abstr. Appl. Anal. 2014, Article ID 636751 (2014). doi:10.1155/2014/636751
Mo, H.: Generalized Hermite-Hadamard inequalities involving local fractional integral. arXiv:1410.1062
Ostrowski, A.M.: Über die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert. Comment. Math. Helv. 10, 226–227 (1938)
Sarikaya, M.Z., Budak, H.: Generalized Ostrowski type inequalities for local fractional integrals. RGMIA Res. Rep. Collect. 18, Article 62, 11 (2015)
Sarikaya, M.Z., Erden, S., Budak, H.: Some generalized Ostrowski type inequalities involving local fractional integrals and applications. RGMIA Res. Rep. Collect. 18, Article 63, 12 (2015)
Sarikaya, M.Z., Budak, H.: On generalized Hermite-Hadamard inequality for generalized convex function. RGMIA Res. Rep. Collect. 18, Article 64, 15 (2015)
Sarikaya, M.Z., Erden, S., Budak, H.: Some integral inequalities for local fractional integrals. RGMIA Res. Rep. Collect. 18, Article 65, 12 (2015)
Sarikaya, M.Z., Budak, H., Erden, S.: On new inequalities of Simpson’s type for generalized convex functions. RGMIA Res. Rep. Collect. 18, Article 66, 13 (2015)
Sarikaya, M.Z., Tunc, T., Budak, H.: On generalized some integral inequalities for local fractional integrals. RGMIA Res. Rep. Collect. 18, Article 87, 13 (2015)
Yang, X.J.: Advanced Local Fractional Calculus and Its Applications. World Science, New York (2012)
Yang, J., Baleanu, D., Yang, X.J.: Analysis of fractal wave equations by local fractional Fourier series method. Adv. Math. Phys. 2013, Article ID 632309 (2013). doi:10.1155/2013/632309
Yang, X.J.: Local fractional integral equations and their applications. Adv. Comput. Sci. Appl. (ACSA) 1(4), 234–239 (2012)
Yang, X.J.: Generalized local fractional Taylor’s formula with local fractional derivative. J. Expert Syst. 1(1), 26–30 (2012)
Yang, X.J.: Local fractional Fourier analysis. Adv. Mech. Eng. Appl. 1(1), 12–16 (2012)
Yang, X.J., Tenreiro Machado, J.A., Srivastava, H.M.: A new numerical technique for solving the local fractional diffusion equation. Appl. Math. Comput. 274, 143–151 (2016)
Yang, X.J., Tenreiro Machado, J.A.: A new insight into complexity from the local fractional calculus view point: modelling growths of populations. Math. Meth. Appl. Sci. (2015). doi:10.1002/mma.3765
Yang, X.J., Tenreiro Machado, J.A., Hristov, J.: Nonlinear dynamics for local fractional Burgers’ equation arising in fractal flow. J. Nonlinear Dyn. 84, 3 (2016). doi:10.1007/s11071-015-2085-2
Yang, X.J., Baleanu, D., Lazarevic, M.P., Cajic, M.S.: Fractal boundary value problems for integral and differential equations with local fractional operators. Thermal Sci. 19(3), 959–966 (2015)
Singh, J., Kumar, D., Nieto, J.J.: A reliable algorithm for a local fractional tricomi equation arising in fractal transonic flow. Entropy 18(6), 206 (2016)
Jafari, H., Jassim, H.K., Tchier, F., Baleanu, D.: On the approximate solutions of local fractional differential equations with local fractional operators. Entropy 18(4), 150 (2016)
Yang, A.M., Li, J., Zhang, Y.Z., Liu, W.X.: A new coupling schedule for series expansion method and sumudu transform with an applications to diffusion equation in fractal heat transfer. Therm. Sci. 19(1), S145–S149 (2015)
Kolwankar, K.M., Gangal, A.D.: Fractional differentiability of nowhere differentiable functions and dimensions. Chaos 6, 505 (1996). doi:10.1063/1.166197
Podlubny, I.: Fractional Differential Equations. Academic, San Diego (1998)
Das, S.: Functional Fractional Calculus. Springer, Berlin (2011). ISBN:978-3-642-20545-3
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Akkurt, A., Sarikaya, M.Z., Budak, H. et al. Generalized Ostrowski type integral inequalities involving generalized moments via local fractional integrals. RACSAM 111, 797–807 (2017). https://doi.org/10.1007/s13398-016-0336-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13398-016-0336-9
Keywords
- Local fractional integrals
- Generalized Ostrowski inequality
- Generalized moments
- Generalized Grüss inequality