Convexity and Monotonicity Analyses for Discrete Fractional Operators with Discrete Exponential Kernes
Keywords:
Discrete Fractional Calculus; Exponential Kernel; Positivity Analysis; Monotonicity Analysis; Convexity Analysis.
Abstract
For discrete fractional operators with exponential kernels, positivity, monotonicity, and convexity findings are taken into consideration in this paper. Our findings cover both sequential and non-sequential scenarios and show how fractional differences with other kinds of kernels and the exponential kernel example are comparable and different. This demonstrates that the qualitative information gathered in the exponential kernel case does not match other situations perfectly.
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References
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23. Atici, Ferhan M., and Paul Eloe. "Discrete fractional calculus with the nabla operator." Electronic Journal of Qualitative Theory of Differential Equations [electronic only] 2009 (2009): Paper-No.
24. Anastassiou, George A. "Nabla discrete fractional calculus and nabla inequalities." Mathematical and Computer Modelling 51, no. 5-6 (2010): 562-571.
2. Magin, R. "Begell House Inc." Fractional Calculus in Bioengineering (2006).
3. Podlubny, I. "Fractional Differential Equations Academic Press, San Diego, 1999.".
4. Smit, W., and H. De Vries. "Rheological models containing fractional derivatives." Rheologica Acta 9, no. 4 (1970): 525-534.
5. Dahal, Rajendra, and Christopher S. Goodrich. "A monotonicity result for discrete fractional difference operators." Archiv der Mathematik 102, no. 3 (2014): 293-299.
6. Goodrich, Christopher S. "A convexity result for fractional differences." Applied Mathematics Letters 35 (2014): 58-62.
7. Jamison, C. E., R. D. Marangoni, and A. A. Glaser. "Viscoelastic properties of soft tissue by discrete model characterization." (1968): 239-247.
8. Coussot, Cecile. "Fractional derivative models and their use in the characterization of hydropolymer and in-vivo breast tissue viscoelasticity." (2008).
9. Kelley, Walter G., and Allan C. Peterson. Difference equations: an introduction with applications. Academic press, 2001.
10. Goodrich, Christopher, and Allan C. Peterson. Discrete fractional calculus. Vol. 1350. Berlin: Springer, 2015.
11. Abdeljawad, Thabet, and Dumitru Baleanu. "Monotonicity results for fractional difference operators with discrete exponential kernels." Advances in Difference Equations 2017, no. 1 (2017): 1-9.
12. Abdeljawad, Thabet, Qasem M. Al-Mdallal, and Mohamed A. Hajji. "Arbitrary order fractional difference operators with discrete exponential kernels and applications." Discrete Dynamics in Nature and Society 2017 (2017).
13. Goodrich, Christopher, and Carlos Lizama. "A transference principle for nonlocal operators using a convolutional approach: Fractional monotonicity and convexity." Israel Journal of Mathematics 236, no. 2 (2020): 533-589.
14. Baoguo, Jia, Lynn Erbe, and Allan Peterson. "Convexity for nabla and delta fractional differences." Journal of Difference Equations and Applications 21, no. 4 (2015): 360-373.
15. Abdeljawad, Thabet. "On Riemann and Caputo fractional differences." Computers & Mathematics with Applications 62, no. 3 (2011): 1602-1611.
16. Abdeljawad, Thabet, and Dumitru Baleanu. "Monotonicity results for fractional difference operators with discrete exponential kernels." Advances in Difference Equations 2017, no. 1 (2017): 1-9.
17. Anastassiou, George A. "Nabla discrete fractional calculus and nabla inequalities." Mathematical and Computer Modelling 51, no. 5-6 (2010): 562-571.
18. Ferreira, Rui AC. "A discrete fractional Gronwall inequality." Proceedings of the American Mathematical Society (2012): 1605-1612.
19. Ferreira, Rui AC. "Existence and uniqueness of solution to some discrete fractional boundary value problems of order less than one." Journal of Difference Equations and Applications 19, no. 5 (2013): 712-718.
20. Dahal, Rajendra, and Christopher S. Goodrich. "A uniformly sharp convexity result for discrete fractional sequential differences." Rocky Mountain Journal of Mathematics 49, no. 8 (2019): 2571-2586.
21. Jia, Baoguo, Lynn Erbe, and Allan Peterson. "Some relations between the Caputo fractional difference operators and integer-order differences." (2015).
22. Baoguo, Jia, Lynn Erbe, and Allan Peterson. "Monotonicity and convexity for nabla fractional q-differences." Dynam. Systems Appl 25, no. 1-2 (2016): 47-60.
23. Atici, Ferhan M., and Paul Eloe. "Discrete fractional calculus with the nabla operator." Electronic Journal of Qualitative Theory of Differential Equations [electronic only] 2009 (2009): Paper-No.
24. Anastassiou, George A. "Nabla discrete fractional calculus and nabla inequalities." Mathematical and Computer Modelling 51, no. 5-6 (2010): 562-571.
Published
2024-06-17
How to Cite
Amirov, S., & Saadullah, I. H. (2024). Convexity and Monotonicity Analyses for Discrete Fractional Operators with Discrete Exponential Kernes. Journal of Progressive Research in Mathematics, 21(1), 1-14. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2225
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