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Year 2020, Volume: 3 Issue: 1, 136 - 140, 15.12.2020

Lütfi Akın , Yusuf Zeren

Abstract

References

  • 1 S.Hilger, Ein Maskettenkalkul mit Anwendung auf Zentrmsmannigfaltingkeiten, Ph.D. Thesis, Univarsi. Wurzburg, 1988.
  • 2 R.P. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: A survey. Math. Inequal. Appl., 4 (2001), 535-555. https://doi.org/10.7153/mia-04-48.
  • 3 E. Akin-Bohner, M. Bohner, F. Akin, Pachpatte inequalities on time scales. Journal of Inequalities in Pure and Applied Mathematics. 6(1) (2005), 1-23.
  • 4 W.N.Li, Nonlinear Integral Inequalities in Two Independent Variables on Time Scales. Adv Differ Equ. (2011), Id:283926. doi:10.1155/2011/283926.
  • 5 G.A. Anastassiou, Principles of delta fractional calculus on time scales and inequalities. Mathematical and Computer Modelling. 52 (2010), 556-566. https://doi.org/10.1016/j.mcm.2010.03.055.
  • 6 F.-H. Wong, C.-C. Yeh, S.-L.Yu, C.-H. Hong, Young’s inequality and related results on time scales, Appl. Math. Lett. 18 (2005), 983-988.
  • 7 F.-H. Wong, C.-C. Yeh, W.-C. Lian, An extension of Jensen’s inequality on time scales, Adv. Dynam. Syst. Appl. 1(1) (2006), 113-120.
  • 8 J. Kuang, Applied inequalities. Shandong Science Press, Jinan, 2003.
  • 9 D. Ucar, V.F. Hatipoglu, A. Akincali,Fractional Integral InequalÄ´sties On TÄ´sme Scales. Open J. Math. Sci., 2(1) (2018), 361-370.
  • 10 U.M. Ozkan, M.Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Appl. Math. Lett., 21 (2008), 993-1000.
  • 11 J.-F. Tian, M.-H. Ha, Extensions of Holder-type inequalities on time scales and their applications, J. Nonlinear Sci. Appl., 10 (2017), 937-953.
  • 12 V. Kac, P. Cheung, Quantum Calculus. Universitext Springer, New York 2002.
  • 13 W.-G. Yang,A functional generalization of diamond-δs integral Holder’s inequality on time scales, Appl. Math. Lett., 23 (2010), 1208-1212.
  • 14 V. Spedding, Taming nature’s numbers,New Scientist, July 1-9 (2003), 28-31.
  • 15 C. C. Tisdell, A. Zaidi,Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling. Nonlinear Anal. 68 (2008), 3504-3524.
  • 16 M. Bohner, J. Heim, A. Liu, Qualitative analysis of Solow model on time scales. J. Concrete Appl. Math., 13 (2015), 183-197.
  • 17 D. Brigo, F. Mercurio, Discrete time vs continuous time stock-price dynamics and implications for option pricing. Finance Stochast., 4 (2000), 147-159.
  • 18 A. R. Seadawy, M. Iqbal and D. Lu, Nonlinear wave solutions of the Kudryashovâ˘A ¸SSinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity,Journal of Taibah University for Science 13(1) (2019), 1060-1072, DOI: 10.1080/16583655.2019.1680170.
  • 19 M. Bohner, R.P. Agarwal,Basic calculus on time scales and some of its applications. Resultate der Mathematic, 35 (1999), 3-22. https://doi.org/10.1007/BF03322019.
  • 20 M. Bohner, A. Peterson,Dynamic equations on time scales, An introduction with applications Birkhauser, Boston, 2001. https://doi.org/10.1007/978-1-4612-0201-1.
  • 21 A. Tuna, S. Kutukcu, Some integral inequalities on time scales. Applied Mathematics and Mechanics (English Edition), 29(1) (2008), 23-28.
  • 22 W. Mingquan, N. Xudong,W. Di and Y. Dunyan, A note on Hardy-Littlewood maximal operators, Journal of Inequalities and Applications, 2016:21 (2016), DOI 10.1186/s13660-016-0963-x.
  • 23 L. Grafakos, Classical and Modern Fourier Analysis. China Machine Press, China (2005).
  • 24 L. AkÄ´sn, On the Fractional Maximal Delta Integral Type Inequalities on Time Scales. Fractal Fract. 4(2) (2020), 1-10.
  • 25 L. Akin, Compactness of Fractional Maximal Operator inWeighted and Variable Exponent Spaces, Erzincan University, Journal of Science and Technology, 12(1) (2019),185-190.
  • 26 L. Akin,On Two Weight Criterions for The Hardy Littlewood Maximal Operator in BFS, Asian Journal of Science and Technology, 9(5)(2018), 8085-8089.

An Investigation on Fractional Maximal Operator in Time Scales

Year 2020, Volume: 3 Issue: 1, 136 - 140, 15.12.2020

Lütfi Akın , Yusuf Zeren

Abstract

Dynamic equations, operators and inequalities have recently increased their motivating role in time scales. Time scales have been the field of study of many mathematicians and scientists working in different sciences for the last 30 years. Dynamic equations and inequalities on time scales have many applications in quantum mechanics, neural networks, heat transfer, electrical engineering, optics, economics and population dynamics. It is possible to give an example from the economics, seasonal investments and incomes. In this research, we will prove that, for $1

Keywords

Time scales variable exponent fractional Maximal operator.

References

  • 1 S.Hilger, Ein Maskettenkalkul mit Anwendung auf Zentrmsmannigfaltingkeiten, Ph.D. Thesis, Univarsi. Wurzburg, 1988.
  • 2 R.P. Agarwal, M. Bohner, A. Peterson, Inequalities on time scales: A survey. Math. Inequal. Appl., 4 (2001), 535-555. https://doi.org/10.7153/mia-04-48.
  • 3 E. Akin-Bohner, M. Bohner, F. Akin, Pachpatte inequalities on time scales. Journal of Inequalities in Pure and Applied Mathematics. 6(1) (2005), 1-23.
  • 4 W.N.Li, Nonlinear Integral Inequalities in Two Independent Variables on Time Scales. Adv Differ Equ. (2011), Id:283926. doi:10.1155/2011/283926.
  • 5 G.A. Anastassiou, Principles of delta fractional calculus on time scales and inequalities. Mathematical and Computer Modelling. 52 (2010), 556-566. https://doi.org/10.1016/j.mcm.2010.03.055.
  • 6 F.-H. Wong, C.-C. Yeh, S.-L.Yu, C.-H. Hong, Young’s inequality and related results on time scales, Appl. Math. Lett. 18 (2005), 983-988.
  • 7 F.-H. Wong, C.-C. Yeh, W.-C. Lian, An extension of Jensen’s inequality on time scales, Adv. Dynam. Syst. Appl. 1(1) (2006), 113-120.
  • 8 J. Kuang, Applied inequalities. Shandong Science Press, Jinan, 2003.
  • 9 D. Ucar, V.F. Hatipoglu, A. Akincali,Fractional Integral InequalÄ´sties On TÄ´sme Scales. Open J. Math. Sci., 2(1) (2018), 361-370.
  • 10 U.M. Ozkan, M.Z. Sarikaya, H. Yildirim, Extensions of certain integral inequalities on time scales, Appl. Math. Lett., 21 (2008), 993-1000.
  • 11 J.-F. Tian, M.-H. Ha, Extensions of Holder-type inequalities on time scales and their applications, J. Nonlinear Sci. Appl., 10 (2017), 937-953.
  • 12 V. Kac, P. Cheung, Quantum Calculus. Universitext Springer, New York 2002.
  • 13 W.-G. Yang,A functional generalization of diamond-δs integral Holder’s inequality on time scales, Appl. Math. Lett., 23 (2010), 1208-1212.
  • 14 V. Spedding, Taming nature’s numbers,New Scientist, July 1-9 (2003), 28-31.
  • 15 C. C. Tisdell, A. Zaidi,Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling. Nonlinear Anal. 68 (2008), 3504-3524.
  • 16 M. Bohner, J. Heim, A. Liu, Qualitative analysis of Solow model on time scales. J. Concrete Appl. Math., 13 (2015), 183-197.
  • 17 D. Brigo, F. Mercurio, Discrete time vs continuous time stock-price dynamics and implications for option pricing. Finance Stochast., 4 (2000), 147-159.
  • 18 A. R. Seadawy, M. Iqbal and D. Lu, Nonlinear wave solutions of the Kudryashovâ˘A ¸SSinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity,Journal of Taibah University for Science 13(1) (2019), 1060-1072, DOI: 10.1080/16583655.2019.1680170.
  • 19 M. Bohner, R.P. Agarwal,Basic calculus on time scales and some of its applications. Resultate der Mathematic, 35 (1999), 3-22. https://doi.org/10.1007/BF03322019.
  • 20 M. Bohner, A. Peterson,Dynamic equations on time scales, An introduction with applications Birkhauser, Boston, 2001. https://doi.org/10.1007/978-1-4612-0201-1.
  • 21 A. Tuna, S. Kutukcu, Some integral inequalities on time scales. Applied Mathematics and Mechanics (English Edition), 29(1) (2008), 23-28.
  • 22 W. Mingquan, N. Xudong,W. Di and Y. Dunyan, A note on Hardy-Littlewood maximal operators, Journal of Inequalities and Applications, 2016:21 (2016), DOI 10.1186/s13660-016-0963-x.
  • 23 L. Grafakos, Classical and Modern Fourier Analysis. China Machine Press, China (2005).
  • 24 L. AkÄ´sn, On the Fractional Maximal Delta Integral Type Inequalities on Time Scales. Fractal Fract. 4(2) (2020), 1-10.
  • 25 L. Akin, Compactness of Fractional Maximal Operator inWeighted and Variable Exponent Spaces, Erzincan University, Journal of Science and Technology, 12(1) (2019),185-190.
  • 26 L. Akin,On Two Weight Criterions for The Hardy Littlewood Maximal Operator in BFS, Asian Journal of Science and Technology, 9(5)(2018), 8085-8089.
There are 26 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Lütfi Akın

Yusuf Zeren

Publication Date December 15, 2020
Acceptance Date September 27, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

APA Akın, L., & Zeren, Y. (2020). An Investigation on Fractional Maximal Operator in Time Scales. Conference Proceedings of Science and Technology, 3(1), 136-140.
AMA Akın L, Zeren Y. An Investigation on Fractional Maximal Operator in Time Scales. Conference Proceedings of Science and Technology. December 2020;3(1):136-140.
Chicago Akın, Lütfi, and Yusuf Zeren. “An Investigation on Fractional Maximal Operator in Time Scales”. Conference Proceedings of Science and Technology 3, no. 1 (December 2020): 136-40.
EndNote Akın L, Zeren Y (December 1, 2020) An Investigation on Fractional Maximal Operator in Time Scales. Conference Proceedings of Science and Technology 3 1 136–140.
IEEE L. Akın and Y. Zeren, “An Investigation on Fractional Maximal Operator in Time Scales”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 136–140, 2020.
ISNAD Akın, Lütfi - Zeren, Yusuf. “An Investigation on Fractional Maximal Operator in Time Scales”. Conference Proceedings of Science and Technology 3/1 (December 2020), 136-140.
JAMA Akın L, Zeren Y. An Investigation on Fractional Maximal Operator in Time Scales. Conference Proceedings of Science and Technology. 2020;3:136–140.
MLA Akın, Lütfi and Yusuf Zeren. “An Investigation on Fractional Maximal Operator in Time Scales”. Conference Proceedings of Science and Technology, vol. 3, no. 1, 2020, pp. 136-40.
Vancouver Akın L, Zeren Y. An Investigation on Fractional Maximal Operator in Time Scales. Conference Proceedings of Science and Technology. 2020;3(1):136-40.
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