References
- Samko SG, Kilbas AA, Maritchev OI. Fractional Integrals and Derivative. Theory and Applications. Gordon & Breach Sci. Publishers; 1987.
- Miller KS, Ross B. An Introduction to the Fractional Calculus and Fractional Differenctial Equations. New York, USA: John Wiley & Sons Inc.; 1993.
- Monje CA, Chen Y, Vinagre BM, Xue D, Fe-liu V. Fractional-order Systems and Controls.London. UK: Springer; 2010.
- Podlubny I. Fractional Differential Equations. Academic Press; 1999.
- Magin R, Ortigueira MD, Podlubny I, Trujillo J. On the fractional signals and systems. Signal Processing. 2011;91(3):350 371. Advances in Fractional Signals and Systems.
- Kilbas AA, Srivastava HM, Trujillo JJ. Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies). USA: Elsevier Science Inc. 2006.
- West BJ. Fractional Calculus and the Future of Science. Entropy. 2021;23(12). https://www.mdpi.com/1099-4300/23/12/1566
- Anastassiou GA. Generalized Fractional Calculus. Springer. Cham. 2021.
- Yang XJ. General Fractional Derivatives: Theory, Methods and Applications. Chapman and Hall/CRC; 2019.
- Tarasov VE. Generalized Memory: Fractional Calculus Approach. Fractal and Fractional. 2018;2(4). https://www.mdpi.com/2504-3110/2/4/23.
- Sierociuk D, Dzielinski A, Sarwas G, Petras I, Podlubny I, Skovranek T. Modelling heat transfer in heterogeneous media using fractional calculus. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2013;371(1990).
- Sakrajda P, Sierociuk D. Modeling Heat Transfer Process in Grid-Holes Structure Changed in Time Using Fractional Variable Order Calculus. In: Babiarz A, Czornik A, Klamka J, Niezabitowski M, editors. Theory and Applications of Non-integer Order Systems. Cham: Springer International Publishing. 2017: 297-306.
- Reyes-Melo ME, Martinez-Vega JJ, Guerrero-Salazar CA, Ortiz-Mendez U. Application of fractional calculus to modelling of relaxation phenomena of organic dielectric materials. In: Proceedings of International Conference on Solid Dielectrics. Toulouse. France: 2004.
- Dzielinski A, Sierociuk D, Sarwas G. Some applications of fractional order calculus. Bulletin of The Polish Academy of Sciences – Technical Sciences. 2010;58(4):583-92.
- Ortigueira MD, Val ério D. Fractional Signals and Systems. De Gruyter; 2020. https://doi.org/10.1515/9783110624588.
- Sheng H, Chen Y, Qiu T. Fractional Processes and Fractional-Order Signal Processing. Springer. London; 2012.
- Muresan CI, Birs IR, Dulf EH, Copot D, Miclea L. A Review of Recent Advances in Fractional-Order Sensing and Filtering Techniques. Sensors. 2021;21(17). Available from: https://www.mdpi.com/1424-8220/21/17/5920.
- Sierociuk D, Tejado I, Vinagre BM. Improved fractional Kalman filter and its application to estimation over lossy networks. Signal Processing. 2011 MAR;91(3, SI):542-52.
- Sierociuk D. Fractional Kalman Filter algorithms for correlated system and measurement noises. Control and Cybernetics. 2013;42(2):471-90.
- Sierociuk D, Ziubinski P. Variable order fractional Kalman filters for estimation over lossy network. Lecture Notes in Electrical Engineering. 2015;320:285-94.
- Wyss W. Fractional noise. Foundations of Physics Letters. 1991;4: 235–246.
- Sierociuk D, Ziubinski P. Fractional order estimation schemes for fractional and integer order systems with constant and variable fractional order colored noise. Circuits, Systems, and Signal Processing. 2014;33(12):3861-82. DOI: 10.1007/s00034-014-9835-0.
- Sierociuk D, Macias M. Triple Estimation of Fractional Variable Order, Parameters, and State Variables Based on the Unscented Fractional Order Kalman Filter. Sensors. 2021;21(23). Available from: https://www.mdpi.com/1424-8220/21/23/8159.
- Macias M, Sierociuk D, Malesza W. MEMS Accelerometer Noises Analysis Based on Triple Estimation Fractional Order Algorithm. Sensors. 2022;22(2).
- Stanislawski R, Latawiec KJ, Lukaniszyn M, Galek M. Time-domain approximations to the Grunwald-Letnikov difference with application to modeling of fractional-order state space systems. In: 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR). 2015: 579-84.
- Stanislawski R, Hunek WP, Latawiec KJ. Finite approximations of a discrete-time fractional derivative. In: 2011 16th International Conference on Methods Models in Automation Robotics. 2011:142-5.
- Sierociuk D, Malesza W, Macias M. Derivation, interpretation, and analog modelling of fractional variable order derivative definition. Applied Mathematical Modelling. 2015;39(13):3876-88. http://dx.doi.org/10.1016/j.apm.2014.12.009.
- Sierociuk D, Malesza W, Macias M. On the Recursive Fractional Variable-Order Derivative: Equivalent Switching Strategy, Duality, and Analog Modeling. Circuits, Systems, and Signal Processing. 2015;34(4):1077-113.
- Macias M, Sierociuk D. An alternative recursive fractional variable-order derivative definition and its analog validation. In: Proceedings of International Conference on Fractional Differentiation and its Applications. Catania, Itally; 2014.
- Ziubinski P, Sierociuk D. Fractional order noise identification with application to temperature sensor data. In: Circuits and Systems (ISCAS), 2015 IEEE International Symposium on; 2015: 2333-6.
- Sierociuk D, Malesza W. Fractional variable order discrete-time systems, their solutions and properties. International Journal of Systems Science. 2017;48(12):3098-105.
- Haykin S. Kalman Filtering and Neural Networks. John Wiley & Sons, Inc.: New York, USA; 2001.
- Sierociuk D. Fractional Variable Order Derivative Simulink Toolkit; 2012. http://www.mathworks.com/matlabcentral/fileexchange/38801-fractional-variable-order-derivative-simulink-toolkit
- Wu B, Cao X. Robust Attitude Tracking Control for Spacecraft with Quantized Torques. IEEE Transactions on Aerospace and Electronic Systems. 2017;11:1-1.
- Wang Y, Yang X, Yan H. Reliable Fuzzy Tracking Control of Near-Space Hypersonic Vehicle Using Aperiodic Measurement Information. IEEE Transactions on Industrial Electronics. 2019;66(12):9439-47.
- Sulochana S, Hablani H. Precision Munition Guidance and Moving-Target Estimation. Journal of Guidance, Control, and Dynamics. 2016;39:1-12.
- Xingling S, Shi Y, Wendong Z. Input-and-Measurement Event-Triggered Output Feedback Chattering Reduction Control for MEMS Gyroscopes. IEEE Transactions on Systems, Man,and Cybernetics: Systems. 2021.
- Xingling S, Shi Y, Wendong Z, Cao H, Jiawei L. Neurodynamic Approximation-Based Quantized Control with Improved Transient Performances for MEMS Gyroscopes: Theory and Experimental Results. IEEE Transactions on Industrial Electronics. 2020.
- Xingling S, Shi Y. Neural-Network-Based Constrained Output-Feedback Control for MEMS Gyroscopes Considering Scarce Transmission Bandwidth. IEEE Transactions on Cybernetics. 2022.
- Xingling S, Si H, Zhang W. Fuzzy wavelet neural control with improved prescribed performance for MEMS gyroscope subject to input quantization. Fuzzy Sets and Systems. 2020;411.