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Aumann, R.J. (1965). Integrals of set-valued functions, Journal of Mathematical Analysis and Applications 12(1): 1–12.10.1016/0022-247X(65)90049-1 Search in Google Scholar

Baake, M. and Schlägel, U. (2011). The Peano–Baker series, Proceedings of the Steklov Institute of Mathematics 275(1): 155–159.10.1134/S0081543811080098 Search in Google Scholar

Balaska, H., Ladaci, S., Djouambi, A., Schulte, H. and Bourouba, B. (2020). Fractional order tube model reference adaptive control for a class of fractional order linear systems, International Journal of Applied Mathematics and Computer Science 30(3): 501–515, DOI: 10.34768/amcs-2020-0037. Search in Google Scholar

Bergounioux, M. and Bourdin, L. (2020). Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints, ESAIM: Control, Optimisation and Calculus of Variations 26: 35, DOI: 10.1051/cocv/2019021.10.1051/cocv/2019021 Search in Google Scholar

Blagodatskikh, V.I. and Filippov, A.F. (1985). Differential inclusions and optimal control, Trudy Matematicheskogo Instituta Imeni VA Steklova 169: 194–252. Search in Google Scholar

Bourdin, L. (2018). Cauchy–Lipschitz theory for fractional multi-order dynamics: State-transition matrices, Duhamel formulas and duality theorems, Differential and Integral Equations 31(7/8): 559–594. Search in Google Scholar

Chikrii, A. and Eidelman, S. (2000). Generalized Mittag-Leffler matrix functions in game problems for evolutionary equations of fractional order, Cybernetics and System Analysis 36(3): 315–338.10.1007/BF02732983 Search in Google Scholar

Chikrii, A. and Matichin, I. (2008). Presentation of solutions of linear systems with fractional derivatives in the sense of Riemann–Liouville, Caputo, and Miller–Ross, Journal of Automation and Information Sciences 40(6): 1–11.10.1615/JAutomatInfScien.v40.i6.10 Search in Google Scholar

Datsko, B. and Gafiychuk, V. (2018). Complex spatio-temporal solutions in fractional reaction-diffusion systems near a bifurcation point, Fractional Calculus and Applied Analysis 21(1): 237–253.10.1515/fca-2018-0015 Search in Google Scholar

Datsko, B., Podlubny, I. and Povstenko, Y. (2019). Time-fractional diffusion-wave equation with mass absorption in a sphere under harmonic impact, Mathematics 7(5): 433.10.3390/math7050433 Search in Google Scholar

Diethelm, K. (2010). The Analysis of Fractional Differential Equations, Springer, Berlin/Heidelberg.10.1007/978-3-642-14574-2 Search in Google Scholar

Dzieliński, A. and Czyronis, P. (2013). Fixed final time and free final state optimal control problem for fractional dynamic systems—Linear quadratic discrete-time case, Bulletin of the Polish Academy of Sciences: Technical Sciences 61(3): 681–690.10.2478/bpasts-2013-0072 Search in Google Scholar

Eckert, M., Nagatou, K., Rey, F., Stark, O. and Hohmann, S. (2019). Solution of time-variant fractional differential equations with a generalized Peano–Baker series, IEEE Control Systems Letters 3(1): 79–84.10.1109/LCSYS.2018.2852600 Search in Google Scholar

Kaczorek, T. (2008). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223–228, DOI: 10.2478/v10006-008-0020-0.10.2478/v10006-008-0020-0 Search in Google Scholar

Kaczorek, T. and Idczak, D. (2017). Cauchy formula for the time-varying linear systems with Caputo derivative, Fractional Calculus and Applied Analysis 20(2): 494–505.10.1515/fca-2017-0025 Search in Google Scholar

Kaczorek, T. and Rogowski, K. (2015). Fractional Linear Systems and Electrical Circuits, Springer, Cham.10.1007/978-3-319-11361-6 Search in Google Scholar

Kamocki, R. (2014). Pontryagin maximum principle for fractional ordinary optimal control problems, Mathematical Methods in the Applied Sciences 37(11): 1668–1686.10.1002/mma.2928 Search in Google Scholar

Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier Science Limited, Amsterdam. Search in Google Scholar

Li, Y., Chen, Y. and Podlubny, I. (2010). Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Computers and Mathematics with Applications 59(5): 1810–1821.10.1016/j.camwa.2009.08.019 Search in Google Scholar

Lorenzo, C.F. and Hartley, T.T. (2000). Initialized fractional calculus, International Journal of Applied Mathematics 3(3): 249–265. Search in Google Scholar

Luchko, Y. (2009). Maximum principle for the generalized time-fractional diffusion equation, Journal of Mathematical Analysis and Applications 351(1): 218–223.10.1016/j.jmaa.2008.10.018 Search in Google Scholar

Malesza, W., Macias, M. and Sierociuk, D. (2019). Analytical solution of fractional variable order differential equations, Journal of Computational and Applied Mathematics 348: 214–236.10.1016/j.cam.2018.08.035 Search in Google Scholar

Martínez, L., Rosales, J., Carreño, C. and Lozano, J. (2018). Electrical circuits described by fractional conformable derivative, International Journal of Circuit Theory and Applications 46(5): 1091–1100.10.1002/cta.2475 Search in Google Scholar

Matychyn, I. (2019). Analytical solution of linear fractional systems with variable coefficients involving Riemann–Liouville and Caputo derivatives, Symmetry 11(11): 1366.10.3390/sym11111366 Search in Google Scholar

Matychyn, I. and Onyshchenko, V. (2015). Time-optimal control of fractional-order linear systems, Fractional Calculus and Applied Analysis 18(3): 687–696.10.1515/fca-2015-0042 Search in Google Scholar

Matychyn, I. and Onyshchenko, V. (2018a). On time-optimal control of fractional-order systems, Journal of Computational and Applied Mathematics 339: 245–257.10.1016/j.cam.2017.10.016 Search in Google Scholar

Matychyn, I. and Onyshchenko, V. (2018b). Optimal control of linear systems with fractional derivatives, Fractional Calculus and Applied Analysis 21(1): 134–150.10.1515/fca-2018-0009 Search in Google Scholar

Matychyn, I. and Onyshchenko, V. (2019). Optimal control of linear systems of arbitrary fractional order, Fractional Calculus and Applied Analysis 22(1): 170–179.10.1515/fca-2019-0011 Search in Google Scholar

Matychyn, I. and Onyshchenko, V. (2020). Solution of linear fractional order systems with variable coefficients, Fractional Calculus and Applied Analysis 23(3): 753–763.10.1515/fca-2020-0037 Search in Google Scholar

Podlubny, I. (1998). Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Academic Press, San Diego. Search in Google Scholar

Rockafellar, R.T. (1970). Convex Analysis, Princeton University Press, Princeton. Search in Google Scholar

Si, X., Yang, H. and Ivanov, I.G. (2021). Conditions and a computation method of the constrained regulation problem for a class of fractional-order nonlinear continuous-time systems, International Journal of Applied Mathematics and Computer Science 31(1): 17–28, DOI: 10.34768/amcs-2021-0002. Search in Google Scholar

Sierociuk, D. and Dzieliński, A. (2006). Fractional Kalman filter algorithm for the states, parameters and order of fractional system estimation, International Journal of Applied Mathematics and Computer Science 16(1): 129–140. Search in Google Scholar

Skovranek, T., Macias, M., Sierociuk, D., Malesza, W., Dzielinski, A., Podlubny, I., Pocsova, J. and Petras, I. (2019). Anomalous diffusion modeling using ultracapacitors in domino ladder circuit, Microelectronics Journal 84: 136–141.10.1016/j.mejo.2019.01.005 Search in Google Scholar

Zorich, V.A. and Paniagua, O. (2016). Mathematical Analysis II, Springer, Berlin/Heidelberg.10.1007/978-3-662-48993-2 Search in Google Scholar

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Mathematics, Applied Mathematics