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ON FUNCTIONAL GENERALIZATION OF OSTROWSKI INEQUALITY FOR CONFORMABLE FRACTIONAL INTEGRALS

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

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.

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

Abstract

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.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

T. Tunç This is me

H. Budak This is me

M. Z. Sarikaya This is me

Publication Date December 1, 2018
Published in Issue Year 2018 Volume: 8 Issue: 2

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