New Ostrowski type inequalities pertaining to conformable fractional operators

Volume 29, Issue 1, pp 28--39 http://dx.doi.org/10.22436/jmcs.029.01.03

Publication Date: August 11, 2022 Submission Date: March 28, 2022 Revision Date: May 25, 2022 Accteptance Date: June 16, 2022

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 510 Downloads
• 1475 Views

Authors

M. Tariq - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan. S. K. Sahoo - Siksha O Anusandhan University, Bhubaneswar, , Odisha, India . H. Ahmad - Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy. A. Iampan - Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. A. A. Shaikh - Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro 76062, Pakistan.

Abstract

The advancements of integral inequalities with the help of fractional operators have recently been the focus of attention in the theory of inequalities. In this study, we first review some fundamental concepts, and then using \(k\)-conformable fractional integrals, we establish a new integral identity for differentiable functions. Then, considering this identity as an auxiliary result, several Ostrowski-type inequalities are presented for functions whose modulus of the first derivatives are quasi-convex. The obtained results represent generalizations as well as refinements for some published results.

Share and Cite

Keywords

• Ostrowski inequality
• quasi-convexity
• \(k\)-fractional conformable integral
• E-beta functions
• E-gamma functions

MSC

•  26A51
•  26A33
•  26D07
•  26D10
•  26D15

References

• [1] M. A. Aba Oud, A. Ali, H. Alrabaiah, S. Ullah, M. A. Khan, S. Islam, A fractional order mathematical model for COVID-19 dynamics with quarantine, isolation, and environmental viral load, Adv. Difference Equ., 2021 (2021), 19 pages
  • View Article
  • MathSciNet


• [2] N. Akhtar, M. U. Awan, M. Z. Javed, M. T. Rassias, M. V. Mihai, M. A. Noor, K. I. Noor, Ostrowski type inequalities involving harmonically convex functions and applications, Symmetry, 13 (2021), 14 pages
  • View Article
  • Google Scholar


• [3] M. Alomari, M. Darus, S. S. Dragomir, P. Cerone, Ostrowski type inequalities for functions whose derivatives are s-convex in the second sense, Appl. Math. Lett., 23 (2010), 1071--1076
  • View Article
  • MathSciNet


• [4] M. S. Alqarni, M. Alghamdi, T. Muhammad, A. S. Alshomrani, M. A. Khan, Mathematical modeling for novel coronavirus (COVID-19) and control, Numer. Methods Partial Differential Equations, 38 (2020), 760--776
  • View Article
  • MathSciNet


• [5] S. I. Araz, Analysis of a COVID-19 model optimal control, stability and simulations, Alex. Eng. J., 60 (2021), 647--658
  • View Article
  • Google Scholar


• [6] A. Atangana, Modelling the spread of COVID-19 with new fractal-fractional operators Can the lockdown save mankind before vaccination?, Chaos Solitons Fractals, 136 (2020), 38 pages
  • View Article
  • MathSciNet


• [7] B. Celik, E. Set, A. O. Akdemir, New inequalities of Ostrowski’s type for quasi-convex functions associated with new fractional conformable integrals, Math. Stud. Appl., 362 (2018), 4--6
  • View Article
  • Google Scholar


• [8] R. Diaz, E. Pariguan, On hypergeometric functions and pochhammer k-symbol, Divulg. Mat., 15 (2007), 179--192
  • View Article
  • MathSciNet
  • MATH


• [9] G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge University Press, Cambridge (1952)
  • View Article
  • Google Scholar


• [10] F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Adv. Difference Equ., 47 (2017), 16 pages
  • View Article
  • MathSciNet
  • MATH


• [11] H. Kadakal, Hermite-Hadamard type inequalities for trigonometrically convex functions, Sci. Stud. Res. Ser. Math. Inform., 28 (2018), 19--28
  • View Article
  • MathSciNet


• [12] M. A. Khan, A. Atangana, E. Alzahrani, Fatmawati, The dynamics of COVID-19 with quarantined and isolation, Adv. Difference Equ., 2020 (2020), 22 pages
  • View Article
  • MathSciNet


• [13] M. A. Khan, Y. M. Chu, T. U. Khan, J. Khan, Some new inequalities of Hermite-Hadamard type for s-convex functions with applications, Open Math., 15 (2017), 1414--1430
  • View Article
  • MathSciNet


• [14] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B.V., Amsterdam (2006)
  • View Article
  • MathSciNet
  • MATH


• [15] B. B. Mohsen, M. U. Awan, M. Z. Javed, M. A. Noor, K. I. Noor, Some new Ostrowski-type inequalities involving σ-fractional integrals, J. Math., 2021 (2021), 12 pages
  • View Article
  • MathSciNet


• [16] S. Mubeen, S. Iqbal, G. Rahman, Contiguous function relations and an integral representation for Appell k-series F(1, k), Int. J. Math. Res., 4 (2015), 53--63
  • View Article
  • Google Scholar


• [17] C. P. Niculescu, L.-E. Persson, Convex functions and their applications, Springer-Verlag, New York (2006)
  • View Article
  • MathSciNet
  • MATH


• [18] A. Ostrowski, Uber die absolutabweichung einer differentierbaren Funktion von ihren Integralmittelwert, Comment. Math. Helv., 10 (1938), 226--227
  • View Article
  • Google Scholar


• [19] S. Özcan, İ. İşcan, Some new Hermite-Hadamard type integral inequalities for the s–convex functions and theirs applications, J. Inequal. Appl., 201 (2019), 1--14
  • View Article
  • Google Scholar


• [20] F. Qi, S. Habib, S. Mubeen, M. N. Naeem, Generalized k-fractional conformable integrals and related inequalities, AIMS Math., 4 (2019), 343--358
  • View Article
  • MathSciNet


• [21] S. K. Sahoo, R. P. Agarwal, P. O. Mohammed, B. Kodamasingh, K. Nonlaopon, K. M. Abualnaja, Hadamard-Mercer, Dragomir-Agarwal-Mercer, and Pachpatte-Mercer Type Fractional Inclusions for Convex Functions with an Exponential Kernel and Their Applications, Symmetry, 14 (2022), 11 pages
  • View Article
  • Google Scholar


• [22] S. K. Sahoo, P. O. Mohammed, B. Kodamasingh, M. Tariq, Y. S. Hamed, New Fractional Integral Inequalities for Convex Functions Pertaining to Caputo-Fabrizio Operator, Fractal Fract., 6 (2022), 13 pages
  • View Article
  • Google Scholar


• [23] E. Set, New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fracional integrals, Comput. Math. Appl., 63 (2012), 1147--1154
  • View Article
  • Google Scholar


• [24] E. Set, B. Celik, Fractional Hermite-Hadamard type inequalities for quasi-convex functions, Ordu Univ. J. Sci. Tech., 2016 (2016), 137--149
  • Google Scholar


• [25] E. Set, M. E. Özdemir, M. Z. Sarikaya, New inequalities of Ostrowski’s type for s-convex functions in the second sense with applications, Facta Univ. Ser. Math. Inform., 2012 (2012), 67--82
  • View Article
  • MathSciNet


• [26] H. M. Srivastava, Some parametric and argument variations of the operators of fractional calculus and related special functions and integral transformations, J. Nonlinear Convex Anal., 22 (2021), 1501--1520
  • Google Scholar


• [27] M. Tariq, New Hermite–Hadamard type inequalities via p–harmonic exponential type convexity and applications, Uni. J. Math. Appl., 4 (2021), 59--69
  • View Article
  • Google Scholar


• [28] M. Tariq, J. Nasir, S. K. Sahoo, A. A. Mallah, A note on some Ostrowski type inequalities via generalized exponentially convex function, J. Math. Anal. Model., 2 (2021), 1--15
  • View Article
  • Google Scholar


• [29] M. Tariq, S. K. Sahoo, J. Nasir, S. K. Awan, Some Ostrowski type integral inequalities using Hypergeometric Functions, J. Frac. Calc. Nonlinear Sys., 2 (2021), 24--41
  • View Article
  • Google Scholar