Fractional Inequalities for Exponentially s-Convex Functions on Time Scales
DOI:
https://doi.org/10.15377/2409-5761.2024.11.7Keywords:
Time scales, Fractional taylor formula, Delta-riemann-liouville integral, Exponentially s-convex functionsAbstract
In this paper, we present new integral inequalities involving exponentially s-convex functions in the second sense on time scales. By utilizing the delta Riemann-Liouville fractional integral and the fractional Taylor formula, we establish upper bounds for functions that are n-times rd-continuously Δ-differentiable with exponentially s-convex properties. Our results provide novel insights into the theory of time scales, bridging the gap between discrete and continuous calculus. The application of fractional calculus on time scales is explored, and several well-known inequalities are employed to derive the main findings. These results have potential implications for further studies in fractional dynamic calculus and other related fields.
AMS Subject Classification: 39A10, 39A11, 39A20.
Downloads
References
Hilger S. Ein MaBkettenkalkul mit Anwendung Zentrumsmannigfaltigkeiten (PhD thesis). Universitat Wurzburg; 1988.
Agarwal RP, Bohner M. Basic calculus on time scales and some of its applications. Results Math. 1999; 35(1): 3-22. https://doi.org/10.1007/BF03322019 DOI: https://doi.org/10.1007/BF03322019
Agarwal R, Bohner M, Peterson A. Inequalities on time scales: A survey. Math Inequal Appl. 2001; 4(3): 535-57. https://doi.org/10.7153/mia-04-48 DOI: https://doi.org/10.7153/mia-04-48
Anastassiou GA. Principles of delta fractional calculus on time scales and inequalities. Math Comput Model. 2010; 52(5-6): 556-66. https://doi.org/10.1016/j.mcm.2010.03.055 DOI: https://doi.org/10.1016/j.mcm.2010.03.055
Georgiev S. Fractional dynamic calculus and fractional dynamic equations on time scales. Springer; 2018. https://doi.org/10.1007/978-3-319-73954-0 DOI: https://doi.org/10.1007/978-3-319-73954-0
Awan M, Noor M, Noor K. Hermite-Hadamard inequalities for exponential convex functions. Appl Math Inf Sci. 2018; 12(3): 405-9. https://doi.org/10.18576/amis/120215 DOI: https://doi.org/10.18576/amis/120215
Bohner M, Peterson A. Dynamic equations on time scales: an introduction with applications. Birkhäuser; 2001. https://doi.org/10.1007/978-1-4612-0201-1 DOI: https://doi.org/10.1007/978-1-4612-0201-1
Georgiev S, Darvish V, Nwaeze ER. Ostrowski type inequalities on time scales. Adv Theory Nonlinear Anal Appl. 2022; 6(4): 502-12. https://doi.org/10.31197/atnaa.1021333 DOI: https://doi.org/10.31197/atnaa.1021333
Mehreen N, Anwar M. Hermite-Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in the second sense with applications. J Inequal Appl. 2019; 2019(1): 92. https://doi.org/10.1186/s13660-019-2047-1 DOI: https://doi.org/10.1186/s13660-019-2047-1
Georgiev S. Integral inequalities on time scales. De Gryuter; 2020. https://doi.org/10.1515/9783110705553 DOI: https://doi.org/10.1515/9783110705553
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Svetlin G. Georgiev, Vahid Darvish
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
All the published articles are licensed under the terms of the Creative Commons Attribution Non-Commercial License (CC BY-NC 4.0) which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.
