References
- Caroll RW, Showalter RE. Singular and degenerate Cauchy problems. New York: Academic Press; 1976.
- Boyarintsev YuE. Methods for solving degenerate systems of ordinary differential equations. Novosibirsk: Nauka Publ.; 1988 (in Russian).
- Chistyakov VF. Algebraic differential operators with finite-dimensional kernel. Novosibirsk: Nauka Publ.; 1996 (in Russian).
- Favini A, Yagi A. Degenerate differential equations in Banach spaces. New York: Marcel Dekker Inc.; 1999.
- Sidorov N, Loginov B, Sinitsyn A, Falaleev M. Lyapunov–Schmidt method in nonlinear analysis and applications. Dordrecht: Kluwer Academic Publ.; 2002.
- Pyatkov SG. Operator theory: nonclassical problems. Utrecht: VSP; 2002.
- Demidenko GV, Uspenskii SV. Partial differential equations and systems not solvable with respect to the highest order derivative. New York: Marcel Dekker Inc.; 2003.
- Sviridyuk GA, Fedorov VE. Linear Sobolev type equations and degenerate semigroups of operators. Utrecht: VSP; 2003.
- Sobolev SL. Selected works. Vols. 1, 2. Novosibirsk: Siberian Branch of RAS Publ.; 2003, 2006 (in Russian).
- Li F, Liang J, Xu HK. Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions. J Math Anal Appl. 2012;391(2):510–525. doi: 10.1016/j.jmaa.2012.02.057
- Debbouche A, Nieto JJ. Sobolev type fractional abstract evolution equations with nonlocal conditions and optimal multi-controls. Appl Math Comput. 2014;245:74–85.
- Debbouche A, Torres DFM. Sobolev type fractional dynamic equations and optimal multi-integral controls with fractional nonlocal conditions. Fract Calc Appl Anal. 2015;18(1):435. doi: 10.1515/fca-2015-0007
- Kostić M. Abstract Volterra integro-differential equations. Boca Raton: CRC Press; 2015.
- Kostić M, Fedorov VE. Disjoint hypercyclic and disjoint topologically mixing properties of degenerate fractional differential equations. Russian Math. 2018;62(7):31–46. doi: 10.3103/S1066369X18070034
- Fedorov VE, Gordievskikh DM. Resolving operators of degenerate evolution equations with fractional derivative with respect to time. Russian Math. 2015;59(1):60–70. doi: 10.3103/S1066369X15010065
- Fedorov VE, Gordievskikh DM, Plekhanova MV. Equations in Banach spaces with a degenerate operator under a fractional derivative. Differ Equ. 2015;51(10):1360–1368. doi: 10.1134/S0012266115100110
- Fedorov VE, Kostić M. Degenerate fractional differential equations in locally convex spaces with a σ-regular pair of operators. Ufa Math J. 2016;8(4):98–110. doi: 10.13108/2016-8-4-98
- Fedorov VE, Plekhanova MV, Nazhimov RR. Degenerate linear evolution equations with the Riemann—Liouville fractional derivative. Siberian Math J. 2018;59(1):136–146. doi: 10.1134/S0037446618010159
- Fedorov VE, Romanova EA, Debbouche A. Analytic in a sector resolving families of operators for degenerate evolution fractional equations. J Math Sci. 2018;228(4):380–394. doi: 10.1007/s10958-017-3629-4
- Fedorov VE, Romanova EA. Inhomogeneous evolution fractional order equation in the sectorial case. Itogi Nauki I Tekhniki Ser Contemporary Math Appl Thematic Rev. 2018;149:103–112.
- Plekhanova MV. Sobolev type equations of time-fractional order with periodical boundary conditions. International Conference on Analysis and Applied Mathematics (ICAAM 2016). AIP Conf. Pro.; 1759(020101); 2016. p. 1–4.
- Plekhanova MV. Nonlinear equations with degenerate operator at fractional Caputo derivative. Math Methods Appl Sci. 2017;40(17):6138–6146. doi: 10.1002/mma.3830
- Plekhanova MV. Distributed control problems for a class of degenerate semilinear evolution equations. J Comput Appl Math. 2017;312:39–46. doi: 10.1016/j.cam.2015.09.034
- Plekhanova MV. Strong solutions to nonlinear degenerate fractional order evolution equations. J Math Sci. 2018;230(1):146–158. doi: 10.1007/s10958-018-3734-z
- Fedorov VE, Avilovich AS. A Cauchy type problem for a degenerate equation with the Riemann—Liouville derivative in the sectorial case. Siberian Math J. 2019;60(2):359–372. doi: 10.1134/S0037446619020162
- Fedorov VE, Avilovich AS, Borel LV. Initial problems for semilinear degenerate evolution equations of fractional order in the sectorial case. In: Area V, Cabada A, Cid JA, editors. Nonlinear analysis and boundary value problems. NABVP 2018; Sep 4–7; Santiago de Compostela, Spain. Cham: Springer Nature Switzerland AG; 2019. p. 41–62. (Springer Proceedings in Mathematics and Statistics; vol. 292).
- Prüss J. Evolutionary integral equations and applications. Basel: Springer; 1993.
- Bajlekova EG. Fractional evolution equations in Banach spaces [Ph.D. thesis]. Eindhoven: University Press Facilities, Eindhoven University of Technology; 2001.
- Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier Science Publishing; 2006.
- Fedorov VE. A class of fractional order semilinear evolutions in Banach spaces. In Integral equations and their applications. Proceeding of University Network Seminar on the occasion of The Third Mongolia — Russia — Vietnam Workshop on NSIDE 2018; 2018 October 27–28; Hung Yen, Viet Nam. Hung Yen: Hanoi Mathematical Society, Hung Yen University of Technology and Education; 2018.
- Triebel H. Interpolation theory, functional spaces, differential operators. Amsterdam: North Holland Publ.; 1978.
- Hassard BD, Kazarinoff ND, Wan Y-HTheory and applications of Hopf bifurcation. Cambridge: Cambridge University Press; 1981.