Research Article
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Year 2020, Volume: 69 Issue: 2, 1057 - 1069, 31.12.2020
https://doi.org/10.31801/cfsuasmas.698841

Abstract

References

  • Abdeljawad, T., Fractional operators with boundary points dependent kernels and integration by parts, Discrete and Continuous Dynamical Systems Series S, 13(3) (2020), 351-375.
  • Baleanu, D., Purohit, S.D., Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators, Abstract and Applied Analysis, 2014 (2014), Article ID 609160, 1--10.
  • Baleanu, D., Purohit, S.D., Prajapati, J.C., Integral inequalities involving generalized Erdélyi-Kober fractional integral operators, Open Mathematics, 14 (2016), 89--99.
  • Chebyshev, P.L., Sur les expressions approximatives des integrales definies par les autres prises entre les mêmes limites, Proc. Math. Soc. Charkov, 2 (1882), 93--98.
  • Curiel, L., Galué, L., A generalization of the integral operators involving the Gauss hypergeometric function, Revista Técnica de la Facultad de Ingeniería Universidad del Zulia, 19(1) (1996), 17--22.
  • Çelik, B., Set, E., Akdemir, A.O., Mixed Conformable Fractional Grüss-Type Inequalities, 2nd International Conference on Life and Engineering Sciences (ICOLES 2019), Book of Abstracts, Istanbul, Turkey, 2019.
  • Dahmani, Z., Mechouar, O. and Brahami, S., Certain inequalities related to the Chebyshev's functional involving a Riemann-Liouville operator, Bull. Math. Anal. Appl., 3(4) (2011), 38--44.
  • Ekinci, A., Özdemir, M.E., Some new integral Inequalities via Riemann Liouville integral operators, Applied and Computational Mathematics, 18(3) (2019), 288--295.
  • Farid, G., Existence of an integral operator and its consequences in fractional and conformable integrals, Open Journal of Mathematical Sciences, 3 (2019), 210--216.
  • Gürbüz, M., Özdemir, M.E., On Some Inequalities for Product of Different Kinds of Convex Functions, Turkish Journal of Science, 5(1) (2020), 23--27.
  • Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2006.
  • Kiryakova, V., Generalized Fractional Calculus and Applications, vol. 301 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1994.
  • Ntouyas, S.K., Purohit, S.D., Tariboon, J., Certain Chebyshev Type Integral Inequalities Involving Hadamard's Fractional Operators, Abstract and Applied Analysis, 2014 (2014), Article ID 249091, 1--7.
  • Özdemir, M.E., Set, E., Akdemir, A.O., Sarıkaya, M.Z., Some new Chebyshev type inequalities for functions whose derivatives belongs to L_{p} spaces, Afrika Matematika, 26 (2015), 1609--1619.
  • Rahman, G., Baleanu, D., Qurashi, M.A., Purohit, S.D., Mubeen, S., Arshad, M., The extended Mittag-Leffler function via fractional calculus, J. Nonlinear Sci. Appl., 10 (2017), 4244--4253.
  • Sarıkaya, M.Z., Alp, N., On Hermite-Hadamard-Fejer type integral inequalities for generalized convex functions via local fractional integrals, Open Journal of Mathematical Sciences, 3(1) (2019), 273--284.
  • Set, E., Özdemir, M.E., Demirbaş, S., Chebyshev type inequalities involving extended generalized fractional integral operators, AIMS Mathematics, 5(4) (2020), 3573--3583.
  • Set, E., New Inequalities of Chebyshev Type for Mixed Conformable Fractional Integral Operators, 2nd International Conference on Life and Engineering Sciences (ICOLES 2019), Book of Abstracts, Istanbul, Turkey, 2019.
  • Srivastava, H.M., Choi, J., Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.

On new integral inequalities using mixed conformable fractional integrals

Year 2020, Volume: 69 Issue: 2, 1057 - 1069, 31.12.2020
https://doi.org/10.31801/cfsuasmas.698841

Abstract

During the past two decades or so, fractional integral operators have been one of the most important tools in the development of inequalities theory. By this means, a lot generalized intergral inequalities involving various the fractional integral operators have been presented in the literature. Very recently, mixed conformable fractional integral operators has been introduced by T. Abdeljawad and with the help of these operators some new integral inequalities are obtained. The main aim of the paper is to establish some new Chebyshev type fractional integral inequalities by using mixed conformable fractional integral operators.

References

  • Abdeljawad, T., Fractional operators with boundary points dependent kernels and integration by parts, Discrete and Continuous Dynamical Systems Series S, 13(3) (2020), 351-375.
  • Baleanu, D., Purohit, S.D., Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators, Abstract and Applied Analysis, 2014 (2014), Article ID 609160, 1--10.
  • Baleanu, D., Purohit, S.D., Prajapati, J.C., Integral inequalities involving generalized Erdélyi-Kober fractional integral operators, Open Mathematics, 14 (2016), 89--99.
  • Chebyshev, P.L., Sur les expressions approximatives des integrales definies par les autres prises entre les mêmes limites, Proc. Math. Soc. Charkov, 2 (1882), 93--98.
  • Curiel, L., Galué, L., A generalization of the integral operators involving the Gauss hypergeometric function, Revista Técnica de la Facultad de Ingeniería Universidad del Zulia, 19(1) (1996), 17--22.
  • Çelik, B., Set, E., Akdemir, A.O., Mixed Conformable Fractional Grüss-Type Inequalities, 2nd International Conference on Life and Engineering Sciences (ICOLES 2019), Book of Abstracts, Istanbul, Turkey, 2019.
  • Dahmani, Z., Mechouar, O. and Brahami, S., Certain inequalities related to the Chebyshev's functional involving a Riemann-Liouville operator, Bull. Math. Anal. Appl., 3(4) (2011), 38--44.
  • Ekinci, A., Özdemir, M.E., Some new integral Inequalities via Riemann Liouville integral operators, Applied and Computational Mathematics, 18(3) (2019), 288--295.
  • Farid, G., Existence of an integral operator and its consequences in fractional and conformable integrals, Open Journal of Mathematical Sciences, 3 (2019), 210--216.
  • Gürbüz, M., Özdemir, M.E., On Some Inequalities for Product of Different Kinds of Convex Functions, Turkish Journal of Science, 5(1) (2020), 23--27.
  • Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2006.
  • Kiryakova, V., Generalized Fractional Calculus and Applications, vol. 301 of Pitman Research Notes in Mathematics Series, Longman Scientific & Technical, Harlow, UK, 1994.
  • Ntouyas, S.K., Purohit, S.D., Tariboon, J., Certain Chebyshev Type Integral Inequalities Involving Hadamard's Fractional Operators, Abstract and Applied Analysis, 2014 (2014), Article ID 249091, 1--7.
  • Özdemir, M.E., Set, E., Akdemir, A.O., Sarıkaya, M.Z., Some new Chebyshev type inequalities for functions whose derivatives belongs to L_{p} spaces, Afrika Matematika, 26 (2015), 1609--1619.
  • Rahman, G., Baleanu, D., Qurashi, M.A., Purohit, S.D., Mubeen, S., Arshad, M., The extended Mittag-Leffler function via fractional calculus, J. Nonlinear Sci. Appl., 10 (2017), 4244--4253.
  • Sarıkaya, M.Z., Alp, N., On Hermite-Hadamard-Fejer type integral inequalities for generalized convex functions via local fractional integrals, Open Journal of Mathematical Sciences, 3(1) (2019), 273--284.
  • Set, E., Özdemir, M.E., Demirbaş, S., Chebyshev type inequalities involving extended generalized fractional integral operators, AIMS Mathematics, 5(4) (2020), 3573--3583.
  • Set, E., New Inequalities of Chebyshev Type for Mixed Conformable Fractional Integral Operators, 2nd International Conference on Life and Engineering Sciences (ICOLES 2019), Book of Abstracts, Istanbul, Turkey, 2019.
  • Srivastava, H.M., Choi, J., Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Barış Çelik 0000-0001-5372-7543

Erhan Set 0000-0003-1364-5396

Publication Date December 31, 2020
Submission Date March 5, 2020
Acceptance Date May 30, 2020
Published in Issue Year 2020 Volume: 69 Issue: 2

Cite

APA Çelik, B., & Set, E. (2020). On new integral inequalities using mixed conformable fractional integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(2), 1057-1069. https://doi.org/10.31801/cfsuasmas.698841
AMA Çelik B, Set E. On new integral inequalities using mixed conformable fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2020;69(2):1057-1069. doi:10.31801/cfsuasmas.698841
Chicago Çelik, Barış, and Erhan Set. “On New Integral Inequalities Using Mixed Conformable Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 2 (December 2020): 1057-69. https://doi.org/10.31801/cfsuasmas.698841.
EndNote Çelik B, Set E (December 1, 2020) On new integral inequalities using mixed conformable fractional integrals. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 2 1057–1069.
IEEE B. Çelik and E. Set, “On new integral inequalities using mixed conformable fractional integrals”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 2, pp. 1057–1069, 2020, doi: 10.31801/cfsuasmas.698841.
ISNAD Çelik, Barış - Set, Erhan. “On New Integral Inequalities Using Mixed Conformable Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/2 (December 2020), 1057-1069. https://doi.org/10.31801/cfsuasmas.698841.
JAMA Çelik B, Set E. On new integral inequalities using mixed conformable fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:1057–1069.
MLA Çelik, Barış and Erhan Set. “On New Integral Inequalities Using Mixed Conformable Fractional Integrals”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 2, 2020, pp. 1057-69, doi:10.31801/cfsuasmas.698841.
Vancouver Çelik B, Set E. On new integral inequalities using mixed conformable fractional integrals. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(2):1057-69.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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