@article(ANDRE20115334, author = {D. Andre and M. Meiler and K. Steiner and Ch. Wimmer and Soczka-Guth, T. and D.U. Sauer}, year = {2011}, title = {{Characterization of High-Power Lithium-Ion Batteries by Electrochemical Impedance Spectroscopy. I.~Experimental Investigation}}, journal = {Journal of Power Sources}, volume = {196}, number = {12}, pages = {5334--5341}, doi = {10.1016/j.jpowsour.2010.12.102}, ) @misc(Chen, author = {Y. Chen}, title = {{Oustaloup-Recursive-Approximation for Fractional Order Differentiators}}, howpublished = {MATLAB Central File Exchange}, url = {www.mathworks.com/matlabcentral/fileexchange/3802-oustaloup-recursive-approximation-for-fractional-order-differentiators}, note = {Accessed: Aug.~14, 2020}, ) @article(Dorjgotov, author = {K. Dorjgotov and H. Ochiai and U. Zunderiya}, year = {2018}, title = {{On Solutions of Linear Fractional Differential Equations and Systems Thereof}}, note = {ArXiv:1803.09063}, ) @inproceedings(Khazali, author = {El-Khazali, R. and I.M. Batiha and S. Momani}, year = {2019}, title = {Approximation of Fractional-Order Operators}, editor = {P. Agarwal and D. Baleanu and Y. Chen and S. Momani and J.A.T. Machado}, booktitle = {Fractional Calculus. ICFDA 2018. Springer Proceedings in Mathematics \& Statistics, vol.~303}, publisher = {Springer Singapore}, address = {Singapore}, pages = {121--151}, doi = {10.1007/978-981-15-0430-3\_8}, ) @article(Garrappa_2015, author = {R. Garrappa}, year = {2015}, title = {{Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions}}, journal = {SIAM Journal on Numerical Analysis}, volume = {53}, number = {3}, pages = {1350--1369}, doi = {10.1137/140971191}, ) @article(Ghosh, author = {U. Ghosh and S. Sarkar and S. Das}, year = {2015}, title = {{Solution of System of Linear Fractional Differential Equations with Modified Derivative of Jumarie Type}}, journal = {American Journal of Mathematical Analysis}, volume = {3}, number = {3}, pages = {72--84}, doi = {10.12691/ajma-3-3-3}, ) @book(Gorenflo:2014, author = {R. Gorenflo and A.A. Kilbas and F. Mainardi and S.V. Rogosin}, year = {2014}, title = {{Mittag-Leffler Functions, Related Topics and Applications}}, publisher = {Springer--Verlag}, address = {Berlin, Heidelberg}, doi = {10.1007/978-3-662-43930-2}, ) @article(Gorenflo_2002, author = {R. Gorenflo and J. Loutchko and Y. Luchko}, year = {2002}, title = {{Computation of the Mittag-Leffler Function and its Derivatives}}, journal = {Fractional Calculus \& Applied Analysis (FCAA)}, volume = {5}, number = {4}, pages = {491--518}, ) @article(Haubold, author = {H.J. Haubold and A.M. Mathai and R.K. Saxena}, year = {2011}, title = {{Mittag-Leffler Functions and Their Applications}}, journal = {Journal of Applied Mathematics}, volume = {2011, 51 pages}, doi = {10.1155/2011/298628}, ) @inproceedings(Rauh_IFAC_2020, author = {E. Hildebrandt and J. Kersten and A. Rauh and H. Aschemann}, year = {2020}, title = {{Robust Interval Observer Design for Fractional-Order Models with Applications to State Estimation of Batteries}}, booktitle = {Proc.~of the 21st IFAC World Congress}, address = {Berlin, Germany}, ) @inproceedings(Kersten2019646, author = {J. Kersten and A. Rauh and H. Aschemann}, year = {2019}, title = {{Transformation of Uncertain Linear Fractional Order Differential Equations Into a Cooperative Form}}, booktitle = {Proc.~of 11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019}, address = {Vienna, Austria}, doi = {10.1016/j.ifacol.2019.12.035}, ) @article(Lyons, author = {R. Lyons and A.S. Vatsala and R. Chiquet}, year = {2017}, title = {{Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results}}, journal = {Mathematics}, volume = {5}, number = {4}, doi = {10.3390/math5040065}, ) @inproceedings(MALTI2015769, author = {R. Malti and S. Victor}, year = {2015}, title = {{CRONE Toolbox for System Identification Using Fractional Differentiation Models}}, booktitle = {Proc.~of 17th IFAC Symposium on System Identification SYSID 2015}, volume = {48}, pages = {769--774}, doi = {10.1016/j.ifacol.2015.12.223}, ) @inproceedings(Ned:2006, author = {N.S. Nedialkov}, year = {2007}, title = {{Interval Tools for ODEs and DAEs}}, booktitle = {{CD-Proc.~of 12th GAMM-IMACS Intl.~Symposium on Scientific Computing, Computer Arithmetic, and Validated Numerics SCAN 2006}}, publisher = {IEEE Computer Society}, address = {Duisburg, Germany}, doi = {10.1109/SCAN.2006.28}, ) @book(Oustaloup, author = {A. Oustaloup}, year = {1995}, title = {{La D\'erivation Non Enti\`ere: Th\'eorie, Synth\`ese et Applications}}, publisher = {Herm\`es}, address = {Paris}, note = {In French}, ) @article(817385, author = {A. {Oustaloup} and F. {Levron} and B. {Mathieu} and F. M. {Nanot}}, year = {2000}, title = {{Frequency-Band Complex Noninteger Differentiator: Characterization and Synthesis}}, journal = {IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications}, volume = {47}, number = {1}, pages = {25--39}, doi = {10.1109/81.817385}, ) @book(Podlubny, author = {I. Podlubny}, year = {1999}, title = {{Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications}}, series = {Mathematics in Science and Engineering}, publisher = {Academic Press}, address = {London}, doi = {10.1016/s0076-5392(99)x8001-5}, ) @article(Rauh_Acta_2020, author = {A. Rauh and J. Kersten}, year = {2020}, title = {{Toward the Development of Iteration Procedures for the Interval-Based Simulation of Fractional-Order Systems}}, journal = {Acta Cybernetica}, doi = {10.14232/actacyb.285660}, ) @inproceedings(Rauh_mmar_2019, author = {A. Rauh and J. Kersten and H. Aschemann}, year = {2019}, title = {{Techniques for Verified Reachability Analysis of Quasi-Linear Continuous-Time Systems}}, booktitle = {Proc.~of 24th Intl.~Conference on Methods and Models in Automation and Robotics}, address = {Miedzyzdroje, Poland}, doi = {10.1109/MMAR.2019.8864648}, ) @inproceedings(Rauh_ECC_2020, author = {A. Rauh and J. Kersten and H. Aschemann}, year = {2020}, title = {{Interval-Based Verification Techniques for the Analysis of Uncertain Fractional-Order System Models}}, booktitle = {Proc.~of the 18th European Control Conference ECC2020}, address = {St.~Petersburg, Russia}, doi = {10.23919/ECC51009.2020.9143758}, ) @inproceedings(Rauh_SCAN14, author = {A. Rauh and R. Westphal and H. Aschemann and E. Auer}, year = {2016}, title = {{Exponential Enclosure Techniques for Initial Value Problems with Multiple Conjugate Complex Eigenvalues}}, editor = {M. Nehmeier and J. Wolff von Gudenberg and W. Tucker}, booktitle = {Scientific Computing, Computer Arithmetic, and Validated Numerics}, publisher = {Springer International Publishing}, address = {Cham}, pages = {247--256}, doi = {10.1007/978-3-319-31769-4\_20}, ) @inproceedings(reuter2016, author = {J. Reuter and E. Mank and H. Aschemann and A. Rauh}, year = {2016}, title = {{Battery State Observation and Condition Monitoring Using Online Minimization}}, booktitle = {Proc.~of 21st Intl.~Conference on Methods and Models in Automation and Robotics}, address = {Miedzyzdroje, Poland}, doi = {10.1109/MMAR.2016.7575313}, ) @article(wang, author = {B. Wang and Z. Liu and S. Li and S. Moura and H. Peng}, year = {2017}, title = {{State-of-Charge Estimation for Lithium-Ion Batteries Based on a Nonlinear Fractional Model}}, journal = {IEEE Trans. on Control Systems Technology}, volume = {25}, number = {1}, pages = {3--11}, doi = {10.1109/TCST.2016.2557221}, ) @article(ZOU2018286, author = {Ch. Zou and L. Zhang and X. Hu and Z. Wang and T. Wik and M. Pecht}, year = {2018}, title = {{A Review of Fractional-Order Techniques Applied to Lithium-Ion Batteries, Lead-Acid Batteries, and Supercapacitors}}, journal = {Journal of Power Sources}, volume = {390}, pages = {286--296}, doi = {10.1016/j.jpowsour.2018.04.033}, )