[1] A. Abdelhakim and J. Tenreiro Machado: A critical analysis of the conformable derivative, Nonlinear Dynamics, 95 (2019), 3063–3073, DOI: 10.1007/s11071-018-04741-5.
[2] K. Balachandran, Y. Zhou and J. Kokila: Relative controllability of fractional dynamical systems with delays in control, Communications in Nonlinear Science and Numerical Simulation, 17 (2012), 3508–3520, DOI: 10.1016/j.cnsns.2011.12.018.
[3] K. Balachandran, J. Kokila, and J.J. Trujillo: Relative controllability of fractional dynamical systems with multiple delays in control, Computers and Mathematics with Apllications, 64 (2012), 3037–3045, DOI: 10.1016/j.camwa.2012.01.071.
[4] P. Duch: Optimization of numerical algorithms using differential equations of integer and incomplete orders, Doctoral dissertation, Lodz University of Technology, 2014 (in Polish).
[5] C. Guiver, D. Hodgson and S. Townley: Positive state controllability of positive linear systems. Systems and Control Letters, 65 (2014), 23–29, DOI: 10.1016/j.sysconle.2013.12.002.
[6] R.E. Gutierrez, J.M. Rosario and J.T. Machado: Fractional order calculus: Basic concepts and engineering applications, Mathematical Problems in Engineering, 2010 Article ID 375858, DOI: 10.1155/2010/375858.
[7] T. Kaczorek: Positive 1D and 2D Systems, Communications and Control Engineering, Springer, London 2002.
[8] T. Kaczorek: Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science, 18 (2008), 223–228, DOI: 10.2478/v10006-008-0020-0.
[9] T. Kaczorek: Positive linear systems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences, 58 (2010), 453–458, DOI: 10.2478/v10175-010-0043-1.
[10] T. Kaczorek: Selected Problems of Fractional Systems Theory, Lecture Notes in Control and Information Science, 411, 2011.
[11] T. Kaczorek: Constructability and observability of standard and positive electrical circuits, Electrical Review, 89 (2013), 132–136.
[12] T. Kaczorek: An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs, Bulletin of the Polish Academy of Sciences: Technical Sciences, 62 (2014), 227–231, DOI: 10.2478/bpasts-2014-0022.
[13] T. Kaczorek: Minimum energy control of fractional positive continuoustime linear systems with bounded inputs, International Journal of Applied Mathematics and Computer Science, 24 (2014), 335–340, DOI: 10.2478/amcs-2014-0025.
[14] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits, Springer, Studies in Systems, Decision and Control, 13 2015.
[15] T. Kaczorek: A class of positive and stable time-varying electrical circuits, Electrical Review, 91 (2015), 121–124. DOI: 10.15199/48.2015.05.29.
[16] T. Kaczorek: Computation of transition matrices of positive linear electrical circuits, BUSES – Technology, Operation, Transport Systems, 24 (2019), 179–184, DOI: 10.24136/atest.2019.147.
[17] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo: Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, 2006.
[18] J. Klamka: Controllability of Dynamical Systems, Kluwer Academic Publishers, 1991.
[19] T.J.Machado,V. Kiryakova and F. Mainardi: Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulation, 6 (2011), 1140–1153, DOI: 10.1016/j.cnsns.2010.05.027.
[20] K.S. Miller and B. Ross: An Introduction to the Fractional Calculus and Fractional Differential Calculus, Villey, 1993.
[21] A. Monje, Y. Chen, B.M. Viagre, D. Xue and V. Feliu: Fractional-order Systems and Controls. Fundamentals and Applications, Springer-Verlag, 2010.
[22] K. Nishimoto: Fractional Calculus: Integrations and Differentiations of Arbitrary Order, University of New Haven Press, 1989.
[23] K.B. Oldham and J. Spanier: The Fractional Calculus, Academic Press, 1974.
[24] I. Podlubny: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, In: Mathematics in Science and Engineering, Academic Press, 1999.
[25] S.G. Samko, A.A. Kilbas and O.I. Marichev: Fractional Integrals and Derivatives: Theory and Applications, Gordan and Breach Science Publishers, 1993.
[26] J. Sabatier, O.P. Agrawal and J.A. Tenreiro Machado: Advances in Fractional Calculus, In: Theoretical Developments and Applications in Physics and Engineering, Springer-Verlag, 2007.
[27] B. Sikora: Controllability of time-delay fractional systems with and without constraints, IET Control Theory & Applications, 10 (2016), 1–8, DOI: 10.1049/iet-cta.2015.0935.
[28] B. Sikora: Controllability criteria for time-delay fractional systems with a retarded state, International Journal of Applied Mathematics and Computer Science, 26 (2016), 521–531, DOI: 10.1515/amcs-2016-0036.
[29] B. Sikora and J. Klamka: Constrained controllability of fractional linear systems with delays in control, Systems and Control Letters, 106 (2017), 9–15, DOI: 10.1016/j.sysconle.2017.04.013.
[30] B. Sikora and J. Klamka: Cone-type constrained relative controllability of semilinear fractional systems with delays, Kybernetika, 53 (2017), 370–381, DOI: 10.14736/kyb-2017-2-0370.
[31] B. Sikora: On application of Rothe’s fixed point theorem to study the controllability of fractional semilinear systems with delays, Kybernetika, 55 (2019), 675–689, DOI: 10.14736/kyb-2019-4-0675.
[32] T. Schanbacher: Aspects of positivity in control theory, SIAM J. Control and Optimization, 27 (1989), 457–475.
[33] B. Trzasko: Reachability and controllability of positive fractional discretetime systems with delay, Journal of Automation Mobile Robotics and Intelligent Systems, 2 (2008), 43–47.
[34] J. Wei: The controllability of fractional control systems with control delay, Computers and Mathematics with Applications, 64 (2012), 3153–3159, DOI: 10.1016/j.camwa.2012.02.065.

[1] S. Abbas, M. Benchohra and G.M. N’Guerekata: Topics in Fractional Differential Equations. Springer, New York, 2012.
[2] R. Almeida, R. Kamocki, A.B. Malinowska and T. Odzijewicz: On the existence of optimal consensus control for the fractional Cucker– Smale model. Archives of Control Sciences, 30(4), (2020), 625–651, DOI: 10.24425/acs.2020.135844.
[3] J.J. Benedetto and W. Czaja: Integration and Modern Analysis. Brikhäuser, Boston, 2009.
[4] N. Bourbaki: Fonctions d’une Variable Réele. Hermann, Paris, 1976.
[5] M. Buslowicz: Robust stability of a class of uncertain fractional order linear systems with pure delay. Archives of Control Sciences, 25(2), (2015), 177–187.
[6] A.I. Daniliu: Impulse Series Method in the Dynamic Analysis of Structures. In: Proceedings of the Eleventh World Conference on Earthquake Engineering, paper no 577, (1996).
[7] S. Das: Functional Fractional Calculus. Second edition, Springer, Berlin, 2011.
[8] L. Debnath and D. Bhatta: Integral Transforms and their Applications. Third edition, CRC Press – Taylor & Francis Group, Boca Raton, 2015.
[9] V.A. Ditkin and A.P. Prudnikov: Integral Transforms and Operational Calculus. Pergamon Press, Oxford, 1965.
[10] G. Doetsch: Handbuch der Laplace-Transformation. Band I, Brikhäuser, Basel, 1950.
[11] D.T. Duc and N.D.V. Nhan: Norm inequalities for new convolutions and their applications. Applicable Analysis and Discrete Mathematics, 9(1), (2015), 168–179, DOI: 10.2298/AADM150109001D.
[12] K.J. Engel and R. Nagel: One-Parameter Semigroups for Linear Evolution Equations. Springer, New York, 2000.
[13] K.J. Engel and R. Nagel: A Short Course on Operator Semigroups. Springer, New York, 2006.
[14] T.M. Flett: Differential analysis. Cambridge University Press, Cambridge, 2008.
[15] J.F. Gomez-Aguilar, H. Yepez-Martinez, C. Calderon-Ramon, I. Cruz- Orduna, R.F. Escobar-Jimenez and V.H. Olivares-Peregrino: Modeling of mass-spring-damper system by fractional derivatives with and without a singular kernel. Entropy, 17(9), (2015), 5340–5343, DOI: 10.3390/e17096289.
[16] M.I. Gomoyunov: Optimal control problems with a fixed terminal time in linear fractional-order systems. Archives of Control Sciences, 30(4), (2020), 721–744, DOI: 10.24425/acs.2020.135849.
[17] R. Gorenflo and F. Mainardi: Fractional calculus: Integral and differential equations of fractional order. In: A. Carpinteri and F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Wien, 1997.
[18] R. Grzymkowski and R. Witula: Complex functions and Laplace transform in examples and problems. Pracownia Komputerowa Jacka Skalmierskiego, Gliwice, 2010, (in Polish).
[19] V.A. Ilin, V.A. Sadovniczij and B.H. Sendov: Mathematical Analysis, Initial Course. Moscow University Press, Moscow, 1985, (in Russian).
[20] V.A. Ilin, V.A. Sadovniczij and B.H. Sendov: Mathematical Analysis, Continuation Course. Moscow University Press, Moscow, 1987, (in Russian).
[21] T. Kaczorek: Realization problem for fractional continuous-time systems. Archives of Control Sciences, 18(1), (2008), 43–58.
[22] T. Kaczorek: A new method for computation of positive realizations of fractional linear continuous-time systems. Archives of Control Sciences, 28(4), (2018), 511–525, DOI: 10.24425/acs.2018.125481.
[23] K.S. Kazakov: Dynamic response of a single degree of freedom (SDOF) system in some special load cases, based on the Duhamel integral. In: Proceedings of the EngOpt 2008: International Conference on Engineering Optimization, Rio de Janeiro, Brazil, 2008.
[24] N.S. Khabeev: Duhamel integral form for the interface heat flux between bubble and liquid. International Journal of Heat andMass Transfer, 50(25), (2007), 5340–5343, DOI: 10.1016/j.ijheatmasstransfer.2007.06.012.
[25] J. Klamka and B. Sikora:Newcontrollability criteria for fractional systems with varying delays. Theory and applications of non-integer order systems in Lecture Notes in Electrical Engineering, 407, (2017), 333–344.
[26] M. Klimek: On Solutions of Linear Fractional Differential Equations of a Variational Type. Wydawnictwo Politechniki Częstochowskiej, Częstochowa, 2009.
[27] M.I. Kontorowicz: The Operator Calculus and Processes in Electrical Systems. Wydawnictwo Naukowo-Techniczne, Warsaw, 1968, (in Polish).
[28] M.I. Krasnov , A.I. Kiselev and G.I. Makarenko: Functions of a Complex Variable, Operational Calculus, and Stability Theory, Problems and Exercises. Mir Publishers, Moscow, 1984.
[29] L.D. Kudryavtsev: Course of Mathematical Analysis. Volume 2, Higher School Press, Moscow, 1988, (in Russian).
[30] M.A. Lavrentev and B.V. Shabat: Methods of the Theory of Functions of a Complex Variable. Nauka, Moscow, 1973, (in Russian).
[31] Sz. Lubecki: Duhamel’s theorem for time-dependent thermal boundary conditions. In: R.B Hetnarski (Ed.), Encyclopedia of Thermal Stresses, Springer Netherlands, New Delhi, 2014.
[32] E. Łobos and B. Sikora: Advanced Calculus – Selected Topics. Silesian University of Technology Press, Gliwice, 2009.
[33] Z. Łuszczki: Application of general Bernstein polynomials to proving some theorem on partial derivatives. Prace Matematyczne, 2(2), (1958), 355–360, (in Polish).
[34] J. Mikusinski: On continuous partial derivatives of function of several variables. Prace Matematyczne, 7(1), (1962), 55–58, (in Polish).
[35] S. Mischler: An introduction to evolution PDEs, Chapter 3 – Evolution Equation and semigroups, Dauphine Université Paris, published online: www.ceremade.dauphine.fr/~mischler/Enseignements/M2evol1516/chap3.pdf.
[36] N.Nguyen Du Vi, D. Dinh Thanh and T. Vu Kim:Weighted norminequalities for derivatives and their applications. Kodai Mathematical Journal, 36(2), (2013), 228–245.
[37] J. Osiowski: An Outline of the Operator Calculus.Wydawnictwo Naukowo- Techniczne, Warsaw, 1981, (in Polish).
[38] G. Petiau: Theory of Bessel’s Functions. Centre National de la Recherche Scientifique, Paris, 1955, (in French).
[39] K. Rogowski: Reachability of standard and fractional continuous-time systems with constant inputs. Archives of Control Sciences, 26(2), (2016), 147–159, DOI: 10.1515/acsc-2016-0008.
[40] F.A. Shelkovnikov and K.G. Takaishvili: Collection of Problems on Operational Calculus. Higher School Press, Moscow, 1976, (in Russian).
[41] B. Sikora: Controllability of time-delay fractional systems with and without constraints. IET Control Theory & Applications, 10(3), (2019), 320–327.
[42] B. Sikora: Controllability criteria for time-delay fractional systems with retarded state. International Journal of Applied Mathematics and Computer Science, 26(6), (2019), 521–531.
[43] B. Sikora and J. Klamka: Constrained controllability of fractional linear systems with delays in control. Systems & Control Letters, 106, (2017), 9–15.
[44] B. Sikora and J. Klamka: Constrained controllability of fractional linear systems with delays in control. Kybernetika, 53(2), (2017), 370–381.
[45] B. Sikora: On application of Rothe’s fixed point theorem to study the controllability of fractional semilinear systems with delays. Kybernetika, 55(4), (2019), 675–698.
[46] B. Sikora and N. Matlok: On controllability of fractional positive continuous-time linear systems with delay. Archives of Control Sciences, 31(1), (2021), 29–51, DOI: 10.24425/acs.2021.136879.
[47] J. Tokarzewski: Zeros and the output-zeroing problem in linear fractionalorder systems. Archives of Control Sciences, 18(4), (2008), 437–451.
[48] S. Umarov: On fractional Duhamel’s principle and its applications. Journal of Differential Equations, 252(10), (2012), 5217–5234.
[49] S. Umarov and E. Saydamatov: A fractional analog of the Duhamel principle. Fractional Calculus & Applied Analysis, 9(1), (2006), 57–70.
[50] S. Umarov and E. Saydamatov: A generalization of Duhamel’s principle for differential equations of fractional order. Doklady Mathematics, 75(1), (2007), 94–96.
[51] C. Villani: Birth of a Theorem, Grasset & Fasquelle, 2012, (in French).