On representation formulas for solutions of linear differential equations with Caputo fractional derivatives

References

[1] T. Atanackovic, D. Dolicanin, S. Pilipovic, and B. Stankovic, Cauchy problems for some classes of linear fractional differential equations. Fract. Calc. Appl. Anal. 17, No 4 (2014), 1039–1059; 10.2478/s13540-014-0213-1; https://www.degruyter.com/view/journals/fca/17/4/fca.17.issue-4.xml.Search in Google Scholar

[2] B. Bonilla, M. Rivero, and J.J. Trujillo, On systems of linear fractional differential equations with constant coefficients. Appl. Math. Comput. 187, No 1 (2007), 68–78; 10.1016/j.amc.2006.08.104.Search in Google Scholar

[3] L. Bourdin, Cauchy–Lipschitz theory for fractional multi-order dynamics: State-transition matrices, Duhamel formulas and duality theorems. Differ. Integral Equ. 31, No 7-8 (2018), 559–594; https://projecteuclid.org/euclid.die/1526004031.10.57262/die/1526004031Search in Google Scholar

[4] L. Bourdin, Weighted Hölder continuity of Riemann–Liouville fractional integrals – Application to regularity of solutions to fractional Cauchy problems with Carathéodory dynamics. Fract. Calc. Appl. Anal. 22, No 3 (2019), 722–749; 10.1515/fca-2019-0040; https://www.degruyter.com/view/journals/fca/22/3/fca.22.issue-3.xml.Search in Google Scholar

[5] A.A. Chikriy and I.I. Matichin, Presentation of solutions of linear systems with fractional derivatives in the sense of Riemann–Liouville, Caputo and Miller–Ross. J. Autom. Inf. Sci. 40, No 6 (2008), 1–11; 10.1615/JAutomatInfScien.v40.i6.10.Search in Google Scholar

[6] N.D. Cong and H.T. Tuan, Generation of nonlocal fractional dynamical systems by fractional differential equations. J. Integral Equations Appl. 29, No 4 (2017), 585–608; 10.1216/JIE-2017-29-4-585.Search in Google Scholar

[7] K. Diethelm, The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type. Volume 2004 of Lecture Notes in Mathematics, Springer-Verlag, Berlin (2010).10.1007/978-3-642-14574-2_8Search in Google Scholar

[8] J. Duan, A generalization of the Mittag-Leffler function and solution of system of fractional differential equations. Adv. Differ. Eq. Art. No 239 (2018); 10.1186/s13662-018-1693-9.Search in Google Scholar

[9] M.I. Gomoyunov, Fractional derivatives of convex Lyapunov functions and control problems in fractional order systems. Frac. Calc. Appl. Anal. 21, No 5 (2018), 1238–1261; 10.1515/fca-2018-0066; https://www.degruyter.com/view/journals/fca/21/5/fca.21.issue-5.xml.Search in Google Scholar

[10] M.I. Gomoyunov, Approximation of fractional order conflict-controlled systems. Progr. Fract. Differ. Appl. 5, No 2 (2019), 143–155; 10.18576/pfda/050205.Search in Google Scholar

[11] M.I. Gomoyunov, Solution to a zero-sum differential game with fractional dynamics via approximations. Dyn. Games Appl. 10, No 2 (2020), 417–443; 10.1007/s13235-019-00320-4.Search in Google Scholar

[12] M.I. Gomoyunov and N.Yu. Lukoyanov, Guarantee optimization in functional-differential systems with a control aftereffect. J. Appl. Math. Mech. 76, No 4 (2012), 369–377; 10.1016/j.jappmathmech.2012.09.002.Search in Google Scholar

[13] M.I. Gomoyunov and N.Yu. Lukoyanov, On the numerical solution of differential games for neutral-type linear systems. Proc. Steklov Inst. Math. 301, Suppl. 1 (2018), 44–56; 10.1134/S0081543818050048.Search in Google Scholar

[14] D. Idczak and R. Kamocki, On the existence and uniqueness and formula for the solution or R–L fractional Cauchy problem in ℝⁿ. Fract. Calc. Appl. Anal. 14, No 4 (2011), 538–553; 10.2478/s13540-011-0033-5; https://www.degruyter.com/view/journals/fca/14/4/fca.14.issue-4.xml.Search in Google Scholar

[15] T. Kaczorek and D. Idczak, Cauchy formula for the time-varying linear systems with Caputo derivative. Fract. Calc. Appl. Anal. 20, No 2 (2017), 494–505; 10.1515/fca-2017-0025; https://www.degruyter.com/view/journals/fca/20/2/fca.20.issue-2.xml.Search in Google Scholar

[16] A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Volume 204 of North-Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006).Search in Google Scholar

[17] A.N. Krasovskii and N.N. Krasovskii, Control under Lack of Information. Birkhäuser, Boston (1995).10.1007/978-1-4612-2568-3Search in Google Scholar

[18] N.N. Krasovskii and N.Yu. Lukoyanov, Problem of conflict control with hereditary information. J. Appl. Math. Mech. 60, No 6 (1996), 869–882; 10.1016/S0021-8928(96)00109-8.Search in Google Scholar

[19] N.Yu. Lukoyanov and M.I. Gomoyunov, Differential games on minmax of the positional quality index. Dyn. Games Appl. 9, No 3 (2019), 780–799; 10.1007/s13235-018-0281-7.Search in Google Scholar

[20] N.Yu. Lukoyanov and T.N. Reshetova, Problems of conflict control of high dimensionality functional systems. J. Appl. Math. Mech. 62, No 4 (1998), 545–554; 10.1016/S0021-8928(98)00071-9.Search in Google Scholar

[21] A.V. Pskhu, Initial-value problem for a linear ordinary differential equation of noninteger order. Sb. Math. 202, No 4 (2011), 571–582; 10.4213/sm7645.Search in Google Scholar

[22] S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives. Theory and Applications. Gordon and Breach Science Publishers, Yverdon (1993).Search in Google Scholar

[23] A. Zahariev and H. Kiskinov, Existence of fundamental matrix for neutral linear fractional system with distributed delays. Int. J. Pure Appl. Math. 119, No 1 (2018), 31–51; 10.12732/ijpam.v119i1.3.Search in Google Scholar

[24] H. Zhang and D. Wu, Variation of constant formulae for time invariant and time varying Caputo fractional delay differential systems. J. Math. Res. Appl. 34, No 5 (2014), 549–560; 10.3770/j.issn:2095-2651.2014.05.006.Search in Google Scholar