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Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals

Year 2022, Volume: 10 Issue: 1, 182 - 187, 15.04.2022

Abstract

The purpose of this work is to establish extended Ostrowski type inequalities involving conformable fractional integrals. We first give an identity for functions whose α-fractional derivatives are bounded. After that, two extended Ostrowski type inequalities which involve conformable fractional integrals for functions whose α-fractional derivatives are bounded are developed. Additionally, the applications of numerical integration that emerged when investigating these inequalities are given.

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279 (2015) 57–66.
  • [2] T. Abdeljawad, M. A. Horani, R. Khalil, Conformable fractional semigroup operators, Journal of Semigroup Theory and Applications, vol. 2015 (2015) Article ID. 7.
  • [3] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications, 13( 3), 2014, 177-183.
  • [4] M. Abu Hammad, R. Khalil, Abel’s formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications, 13( 3), 2014, 177-183.
  • [5] D. R. Anderson, Taylor’s formula and integral inequalities for conformable fractional derivatives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, to appear.
  • [6] P. Cerone, S. S. Dragomir and J. Roumeliotis. An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications. RGMIA Research Report Collection, Vol.1 No.1:Art.4 1998.
  • [7] S. S. Dragomir. A functional generalization of Ostrowski inequality via Montgomery identity. Acta Math. Univ. Comenian (N.S.), 84(1):63–78, 2015.
  • [8] S. S. Dragomir and N. S. Barnett. An ostrowski type inequality for mappings whose second derivatives are bounded and applications. RGMIA Research Report Collection, V.U.T., 1 (2): 67-76, 1999.
  • [9] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L fpg - norm and applications to some special means and to some numerical quadrature rules. Tamkang J. of Math., 28, (1997), 239-244.
  • [10] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L1 -norm and applications to some special means and to some numerical quadrature rules. Indian Journal of Mathematics, 40 (3), (1998), 299-304.
  • [11] S. S. Dragomir and R. P. Agarwal. Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5): 91-95, 1998.
  • [12] S. S. Dragomir, P. Cerone and J. Roumeliotis. A new generalization of Ostrowski’s integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means. Applied Mathematics Letters, 13: 19-25.
  • [13] S. S. Dragomir and A. Sofo. An integral inequality for twice differentiable mappings and applications. Tamk. J. Math., 31(4), 2000.
  • [14] S. Erden, H. Budak and M. Z. Sarikaya, An Ostrowski Type Inequality for Twice Differentiable Mappings and Applications, Mathematical Modelling and Analysis, 21 (4), 2016, 522-532.
  • [15] M. A. Khan, S. Begum, Y. Khurshid and Y. M.Chu, Ostrowski type inequalities involving conformable fractional integrals. Journal of Inequalities and Applications 2018.1 (2018): 1-14.
  • [16] O.S. Iyiola and E. R. Nwaeze, Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122, 2016.
  • [17] R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [18] Z. Liu. Some Ostrowski type inequalities. Mathematical and Computer Modelling, 48:949-960, 2008.
  • [19] A. M. Ostrowski. U¨ ber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert. Comment. Math. Helv. 10:226-227, 1938.
  • [20] M. Z. Sarikaya. On the Ostrowski type integral inequality. Acta Math. Univ. Comenianae, Vol.LXXIX No.1:129-134, 2010.
  • [21] M. Z. Sarikaya. On the Ostrowski type integral inequality for double integrals. Demonstratio Mathematica, Vol.XLV No.3:533-540, 2012.
  • [22] F. Usta, H. Budaki T. Tunc¸ and M. Z. Sarıkaya, New bounds for the Ostrowski type inequalities via conformable fractional calculus. Arabian Journal of Matheamtics, 7: 317-328.
Year 2022, Volume: 10 Issue: 1, 182 - 187, 15.04.2022

Abstract

References

  • [1] T. Abdeljawad, On conformable fractional calculus, Journal of Computational and Applied Mathematics, 279 (2015) 57–66.
  • [2] T. Abdeljawad, M. A. Horani, R. Khalil, Conformable fractional semigroup operators, Journal of Semigroup Theory and Applications, vol. 2015 (2015) Article ID. 7.
  • [3] M. Abu Hammad, R. Khalil, Conformable fractional heat differential equations, International Journal of Differential Equations and Applications, 13( 3), 2014, 177-183.
  • [4] M. Abu Hammad, R. Khalil, Abel’s formula and wronskian for conformable fractional differential equations, International Journal of Differential Equations and Applications, 13( 3), 2014, 177-183.
  • [5] D. R. Anderson, Taylor’s formula and integral inequalities for conformable fractional derivatives, Contributions in Mathematics and Engineering, in Honor of Constantin Caratheodory, Springer, to appear.
  • [6] P. Cerone, S. S. Dragomir and J. Roumeliotis. An inequality of Ostrowski type for mappings whose second derivatives are bounded and applications. RGMIA Research Report Collection, Vol.1 No.1:Art.4 1998.
  • [7] S. S. Dragomir. A functional generalization of Ostrowski inequality via Montgomery identity. Acta Math. Univ. Comenian (N.S.), 84(1):63–78, 2015.
  • [8] S. S. Dragomir and N. S. Barnett. An ostrowski type inequality for mappings whose second derivatives are bounded and applications. RGMIA Research Report Collection, V.U.T., 1 (2): 67-76, 1999.
  • [9] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L fpg - norm and applications to some special means and to some numerical quadrature rules. Tamkang J. of Math., 28, (1997), 239-244.
  • [10] S. S. Dragomir and S. Wang, A new inequality of Ostrowski’s type in L1 -norm and applications to some special means and to some numerical quadrature rules. Indian Journal of Mathematics, 40 (3), (1998), 299-304.
  • [11] S. S. Dragomir and R. P. Agarwal. Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. lett., 11(5): 91-95, 1998.
  • [12] S. S. Dragomir, P. Cerone and J. Roumeliotis. A new generalization of Ostrowski’s integral inequality for mappings whose derivatives are bounded and applications in numerical integration and for special means. Applied Mathematics Letters, 13: 19-25.
  • [13] S. S. Dragomir and A. Sofo. An integral inequality for twice differentiable mappings and applications. Tamk. J. Math., 31(4), 2000.
  • [14] S. Erden, H. Budak and M. Z. Sarikaya, An Ostrowski Type Inequality for Twice Differentiable Mappings and Applications, Mathematical Modelling and Analysis, 21 (4), 2016, 522-532.
  • [15] M. A. Khan, S. Begum, Y. Khurshid and Y. M.Chu, Ostrowski type inequalities involving conformable fractional integrals. Journal of Inequalities and Applications 2018.1 (2018): 1-14.
  • [16] O.S. Iyiola and E. R. Nwaeze, Some new results on the new conformable fractional calculus with application using D’Alambert approach, Progr. Fract. Differ. Appl., 2(2), 115-122, 2016.
  • [17] R. Khalil, M. Al horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, Journal of Computational Apllied Mathematics, 264 (2014), 65-70.
  • [18] Z. Liu. Some Ostrowski type inequalities. Mathematical and Computer Modelling, 48:949-960, 2008.
  • [19] A. M. Ostrowski. U¨ ber die absolutabweichung einer differentiebaren funktion von ihrem integralmitelwert. Comment. Math. Helv. 10:226-227, 1938.
  • [20] M. Z. Sarikaya. On the Ostrowski type integral inequality. Acta Math. Univ. Comenianae, Vol.LXXIX No.1:129-134, 2010.
  • [21] M. Z. Sarikaya. On the Ostrowski type integral inequality for double integrals. Demonstratio Mathematica, Vol.XLV No.3:533-540, 2012.
  • [22] F. Usta, H. Budaki T. Tunc¸ and M. Z. Sarıkaya, New bounds for the Ostrowski type inequalities via conformable fractional calculus. Arabian Journal of Matheamtics, 7: 317-328.
There are 22 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Samet Erden

Pınar Bolu 0000-0002-1757-8381

Publication Date April 15, 2022
Submission Date January 29, 2022
Acceptance Date February 2, 2022
Published in Issue Year 2022 Volume: 10 Issue: 1

Cite

APA Erden, S., & Bolu, P. (2022). Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals. Konuralp Journal of Mathematics, 10(1), 182-187.
AMA Erden S, Bolu P. Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals. Konuralp J. Math. April 2022;10(1):182-187.
Chicago Erden, Samet, and Pınar Bolu. “Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals”. Konuralp Journal of Mathematics 10, no. 1 (April 2022): 182-87.
EndNote Erden S, Bolu P (April 1, 2022) Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals. Konuralp Journal of Mathematics 10 1 182–187.
IEEE S. Erden and P. Bolu, “Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals”, Konuralp J. Math., vol. 10, no. 1, pp. 182–187, 2022.
ISNAD Erden, Samet - Bolu, Pınar. “Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals”. Konuralp Journal of Mathematics 10/1 (April 2022), 182-187.
JAMA Erden S, Bolu P. Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals. Konuralp J. Math. 2022;10:182–187.
MLA Erden, Samet and Pınar Bolu. “Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals”. Konuralp Journal of Mathematics, vol. 10, no. 1, 2022, pp. 182-7.
Vancouver Erden S, Bolu P. Extended Ostrowski Type Inequalities Involving Conformable Fractional Integrals. Konuralp J. Math. 2022;10(1):182-7.
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