
AIMS Mathematics, 2019, 4(3): 714720. doi: 10.3934/math.2019.3.714.
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Proof of the completeness of the system of eigenfunctions for one boundaryvalue problem for the fractional differential equation
1 Department of Mathematical Methods and Computer Technologies, National Research University Higher School of Economics, Myasnitskaya st., 20, 101000, Moscow, Russia
2 Department of Informational Technologies, Moscow Technical University of Communications and Informatics, Aviamotornaya st. 8, 111024, Moscow, Russia
3 Department of Applied Mathematics , National Research Moscow State University of Civil Engineering, Yaroslavskoye highway 26, 129337, Moscow, Russia
Received: , Accepted: , Published:
Special Issues: Initial and Boundary Value Problems for Differential Equations
Keywords: MittagLeffler function; spectrum; eigenvalue; fractional derivative; completeness
Citation: Mukhamed Aleroev, Hedi Aleroeva, Temirkhan Aleroev. Proof of the completeness of the system of eigenfunctions for one boundaryvalue problem for the fractional differential equation. AIMS Mathematics, 2019, 4(3): 714720. doi: 10.3934/math.2019.3.714
References:
 1.T. S. Aleroev and H. T. Aleroeva, On a class of nonselfadjoint operators, corresponding to differential equations of fractional order, Russ. Math., 58 (2014), 312.
 2.T. S. Aleroev, Completeness of the system of eigenfunctions of a fractionalorder differential operator, Differ. Equations, 36 (2000), 918919.
 3.T. S. Aleroev, BoundaryValue Problems for Differential Equations with Fractional Derivatives, Doctoral Degree Thesis, University Moscow State University of Civil Engineering, Moscow, 2000.
 4.T. S. Aleroev, H. T. Aleroeva, N. M. Nie, et al. Boundary value problems for differential equations of fractional order, Mem. Diff. Equ. Math. Phys., 49 (2010), 1982.
 5.T. S. Aleroev, H. T. Aleroeva, J. Huang, et al. Boundary value problems of fractional FokkerPlanck equations, Comput. Math. Appl., 73 (2017), 959969.
 6.M. S. Livshits, On spectral decomposition of linear nonselfadjoint operators, Mat. Sb. (N.S.), 34 (1954), 145199.
 7.M. M. Dzhrbashyan, The boundaryvalue problem for a differential fractionalorder operator of the Sturm–Liouville type, Izv. Akad. Nauk ArmSSR, Ser. Mat., 5 (1970), 7196.
 8.A. V. Agibalova, On the completeness of a system of eigenfunctions and associated functions of differential operators of the orders $(2\varphi)$ and $(1\varphi)$, J. Math. Sci., 174 (2011), 425436.
 9.A. V. Agibalova, On the completeness of the systems of root functions of a fractionalorder differential operator with matrix coefficients, Mat. Zametki, 88 (2010), 317320.
 10.M. M. Malamud, Similarity of Volterra operators and related problems in the theory of differential equations of fractional orders (Russian), translation in Trans. Moscow Math. Soc., 55 (1994), 57122.
 11.M. M. Malamud and L. L. Oridoroga, Analog of the Birkhoff theorem and the completeness results for fractional order differential equations, Russ. J. Math. Phys., 8 (2001), 287308.
 12.M. M. Malamud and L. L. Oridoroga, On some questions of the spectral theory of ordinary differential fractionalorder equation, Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki, 9 (1998), 3947.
 13.M. M. Malamud, Spectral theory of fractional order integration operators, their direct sums, and similarity problem to these operators of their weak perturbations, In: Kochubei, A., Luchko, Y. Editors, Handbook of Fractional Calculus with Applications. Volume 1: Basic Theory, Berlin, Boston: Walter de Gruyter GmbH, 2019.
 14.T. S. Aleroev, On one class of operators associated with differential equations of fractional order, Sib. Mat. Zh., 46 (2005), 963968.
 15.T. S. Aleroev and H. T. Aleroeva, Problems of SturmLiouville type for differential equations with fractional derivatives, In: Kochubei, A., Luchko Y. Editors, Handbook of Fractional Calculus with Applications. Volume 4: Fractional Differential Equations, Berlin, Boston: De Gruyter, 2019.
 16.M. M. Dzhrbashian, The boundaryvalue problem for a differential fractionalorder operator of the SturmLiouville type, Izv. Akad. Nauk ArmSSR, Ser. Mat., 5 (1970), 7196.
 17.T. S. Aleroev, Boundary value problems for differential equations of fractional order, Sib. Electr. Mat.Izv., 10 (2013), 4155.
 18.P. Ma, Y. Li and J. Zhang, Symmetry and nonexistence of positive solutions for fractional systems, Commun. Pure Appl. Anal., 17 (2018), 10531070.
 19.P. Ma and J. Zhang, Existence and multiplicity of solutions for fractional Choquard equations, Nonlinear Anal., 164 (2017), 100117.
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