[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).