ON FUNCTIONAL GENERALIZATION OF OSTROWSKI INEQUALITY FOR CONFORMABLE FRACTIONAL INTEGRALS

Year 2018, Volume: 8 Issue: 2, 495 - 508, 01.12.2018

T. Tunç H. Budak M. Z. Sarikaya

Abstract

In this study, we establish a generalized Ostrowski type integral inequality for conformable fractional integrals. We also give some applications for p-norms and exponential.

Keywords

Ostrowski inequality, conformable fractional integral, Hölder inequality, p- norm, exponential.

References

• [1] Abdeljawad T, (2015), On conformable fractional calculus, Journal of Computational and Applied Mathematics; 279: 57–66.
• [2] Anderson DR, Taylor’s formula and integral inequalities for conformable fractional derivatives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, to appear.
• [3] D. R. Anderson and D. J., (2016), Ulness, Results for conformable differential equations, preprint.
• [4] A. Atangana, D. Baleanu, and A. Alsaedi, (2016), New properties of conformable derivative, Open Math.13: 889–898.
• [5] S. S. Dragomir, (2015), A functiona generalization of Ostrowski inequality via Montgomery identity, Acta Math. Univ. Comenianae, LXXXIV(1), pp. 63-78.
• [6] M.A. Hammad and R. Khalil,(2014), Conformable fractional heat differential equations, International Journal of Differential Equations and Applications, 13: 177-183.
• [7] M.A. Hammad and R. Khalil,(2014), Abel’s formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Application,13: 177-183.
• [8] Iyiola OS and Nwaeze ER, (2016), Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl. 2: 115-122.
• [9] U. Katugampola, A new fractional derivative with classical properties, ArXiv:1410.6535v2.
• [10] 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.
• [11] A. M. Ostrowski, (1938), Uber die absolutabweichung einer differentiebaren funktion von ihrem inte- ¨ gralmitelwert, Comment. Math. Helv. 10, 226-227.
• [12] M.Z. Sarikaya, (2016), Gronwall type inequality for conformable fractional integrals , Konuralp Journal of Mathematics 4(2) 2 pp. 217–222
• [13] F. Usta and M.Z. Sarikaya, (2016), On generalization conformable fractional integral inequalities, preprint.
• [14] M.Z. Sarikaya and F. Usta, (2016), On Comparison Theorems for Conformable Fractional Differential Equations, International Journal of Analysis and Applications 12(2), 207-214.
• [15] M.Z. Sarikaya and H. Budak, New inequalities of Opial Type for conformable fractional integrals, Turkish Journal of Mathematics, in press.
• [16] F. Usta and M. Z. Sarikaya, Explicit Bounds on Certain Integral Inequalities via Conformable Fractional Calculus, Cogent Mathematics, in press.
• [17] A. Zheng, Y. Feng and W. Wang, (2015), The Hyers-Ulam stability of the conformable fractional differential equation, Mathematica Aeterna, Vol. 5, no. 3, 485-492.