Inequalities for Riemann–Liouville-Type Fractional Derivatives of Convex Lyapunov Functions and Applications to Stability Theory
Author
Abstract
Suggested Citation
Download full text from publisher
References listed on IDEAS
- Watcharin Chartbupapan & Ovidiu Bagdasar & Kanit Mukdasai, 2020. "A Novel Delay-Dependent Asymptotic Stability Conditions for Differential and Riemann-Liouville Fractional Differential Neutral Systems with Constant Delays and Nonlinear Perturbation," Mathematics, MDPI, vol. 8(1), pages 1-10, January.
- Yuri Luchko, 2022. "Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense," Mathematics, MDPI, vol. 10(6), pages 1-24, March.
- Erdal Korkmaz & Abdulhamit Ozdemir & Kenan Yildirim & A. Hussain, 2022. "Asymptotical Stability of Riemann-Liouville Nonlinear Fractional Neutral Neural Networks with Time-Varying Delays," Journal of Mathematics, Hindawi, vol. 2022, pages 1-13, September.
- Gao, Xin & Yu, Juebang, 2005. "Chaos in the fractional order periodically forced complex Duffing’s oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1097-1104.
- Shuo Zhang & Yongguang Yu & Wei Hu, 2014. "Robust Stability Analysis of Fractional-Order Hopfield Neural Networks with Parameter Uncertainties," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-14, April.
- Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007.
"Fractional diffusion models of option prices in markets with jumps,"
Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
- Alvaro Cartea & Diego del-Castillo-Negrete, 2006. "Fractional Diffusion Models of Option Prices in Markets with Jumps," Birkbeck Working Papers in Economics and Finance 0604, Birkbeck, Department of Economics, Mathematics & Statistics.
- Chuan-Yun Gu & Feng-Xia Zheng & Babak Shiri, 2021. "Mittag-Leffler Stability Analysis Of Tempered Fractional Neural Networks With Short Memory And Variable-Order," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-12, December.
- Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2021. "Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Jingwei Deng & Weiyuan Ma & Kaiying Deng & Yingxing Li, 2020. "Tempered Mittag–Leffler Stability of Tempered Fractional Dynamical Systems," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, May.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Andrey Itkin & Peter Carr, 2012.
"Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models,"
Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 63-104, June.
- Andrey Itkin & Peter Carr, 2010. "Using pseudo-parabolic and fractional equations for option pricing in jump diffusion models," Papers 1002.1995, arXiv.org.
- Xu Guo & Yutian Li, 2016. "Valuation of American options under the CGMY model," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1529-1539, October.
- Weilong Fu & Ali Hirsa, 2019. "A fast method for pricing American options under the variance gamma model," Papers 1903.07519, arXiv.org.
- Álvaro Cartea, 2013.
"Derivatives pricing with marked point processes using tick-by-tick data,"
Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 111-123, January.
- Cartea, Álvaro, 2010. "Derivatives pricing with marked point processes using Tick-by-tick data," DEE - Working Papers. Business Economics. WB wb101604, Universidad Carlos III de Madrid. Departamento de EconomÃa de la Empresa.
- Jean-Philippe Aguilar & Jan Korbel & Nicolas Pesci, 2021. "On the Quantitative Properties of Some Market Models Involving Fractional Derivatives," Mathematics, MDPI, vol. 9(24), pages 1-24, December.
- Zitane, Hanaa & Torres, Delfim F.M., 2023. "Finite time stability of tempered fractional systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
- Chen, Wen & Wang, Song, 2017. "A power penalty method for a 2D fractional partial differential linear complementarity problem governing two-asset American option pricing," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 174-187.
- H. Ghafouri & M. Ranjbar & A. Khani, 2020. "The Use of Partial Fractional Form of A-Stable Padé Schemes for the Solution of Fractional Diffusion Equation with Application in Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 695-709, December.
- Mancini, Cecilia, 2011. "The speed of convergence of the Threshold estimator of integrated variance," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 845-855, April.
- Buchmann, Boris & Kaehler, Benjamin & Maller, Ross & Szimayer, Alexander, 2017. "Multivariate subordination using generalised Gamma convolutions with applications to Variance Gamma processes and option pricing," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2208-2242.
- Young Shin Kim, 2018. "First Passage Time for Tempered Stable Process and Its Application to Perpetual American Option and Barrier Option Pricing," Papers 1801.09362, arXiv.org.
- Ge, Zheng-Ming & Yi, Chang-Xian, 2007. "Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 42-61.
- Constantinos Kardaras, 2009. "No‐Free‐Lunch Equivalences For Exponential Lévy Models Under Convex Constraints On Investment," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 161-187, April.
- Dilip B. Madan & Wim Schoutens & King Wang, 2017. "Measuring And Monitoring The Efficiency Of Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
- Lynn Boen & Florence Guillaume, 2020. "Towards a $$\Delta $$Δ-Gamma Sato multivariate model," Review of Derivatives Research, Springer, vol. 23(1), pages 1-39, April.
- Yongxin Yang & Yu Zheng & Timothy M. Hospedales, 2016. "Gated Neural Networks for Option Pricing: Rationality by Design," Papers 1609.07472, arXiv.org, revised Mar 2020.
- Fu, Qi & So, Jacky Yuk-Chow & Li, Xiaotong, 2024. "Stable paretian distribution, return generating processes and habit formation—The implication for equity premium puzzle," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
- Álvaro Cartea & Thilo Meyer-Brandis, 2010.
"How Duration Between Trades of Underlying Securities Affects Option Prices,"
Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
- Cartea, Álvaro & Meyer-Brandis, Thilo, 2009. "How Duration Between Trades of Underlying Securities Affects Option Prices," MPRA Paper 16179, University Library of Munich, Germany.
- José Azevedo‐Pereira & Gualter Couto & Cláudia Nunes, 2010. "Optimal timing of relocation," International Journal of Managerial Finance, Emerald Group Publishing Limited, vol. 6(2), pages 143-163, April.
- Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
More about this item
Keywords
Riemann–Liouville-type fractional derivative; tempered fractional derivative; fractional derivative with respect to another function; Lyapunov functions; Mittag–Leffler stability in time;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3859-:d:1236455. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.