Keywords
Fractional taylor formula
Delta-riemann-liouville integral
Exponentially s-convex functions
How to Cite
Abstract
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.
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
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
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
Georgiev S. Fractional dynamic calculus and fractional dynamic equations on time scales. Springer; 2018. 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
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
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
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
Georgiev S. Integral inequalities on time scales. De Gryuter; 2020. https://doi.org/10.1515/9783110705553
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Copyright (c) 2024 Svetlin G. Georgiev, Vahid Darvish