The issues of well-posedness of linear inverse coefficient problems for multi-term equations in Banach spaces with fractional Riemann – Liouville derivatives and with bounded operators at them are considered. Well-posedness criteria are obtained both for the equation resolved with respect to the highest fractional derivative, and in the case of a degenerate operator at the highest derivative in the equation. Two essentially different cases are investigated in the degenerate problem: when the fractional part of the order of the second-oldest derivative is equal to or different from the fractional part of the order of the highest fractional derivative. Abstract results are applied in the study of inverse problems for partial differential equations with polynomials from a self-adjoint elliptic differential operator with respect to spatial variables and with Riemann – Liouville derivatives in time.

Mikhail Turov, Postgraduate, Chelyabinsk State University, 129, Bratiev Kashirinykh st., Chelyabinsk, 454001, Russian Federation, tel.: (351)799-72-35, email: turov m m@mail.ru

Vladimir Fedorov, Dr. Sci. (Phys.–Math.), Prof., Chelyabinsk State University, 129, Bratiev Kashirinykh st., Chelyabinsk, 454001, Russian Federation, tel.: (351)799-72-35, email: kar@csu.ru

Bui Trong Kien, PhD, Doctor in Mathematics, Institute of Mathematics of Vietnam Academy of Science and Technology, 18, Hoang Quoc Viet road, Cau Giay district, Hanoi, Vietnam, tel.: 84 024 375-634-74, email: btkien@math.ac.vn

Turov M.M., Fedorov V.E., Kien B.T. Linear Inverse Problems for Multi-term Equation with Riemann – Liouville Derivatives. The Bulletin of Irkutsk State University. Series Mathematics, 2021, vol. 38, pp. 36-53. https://doi.org/10.26516/1997-7670.2021.38.36

1. Glushak A.V. On an Inverse Problem for an Abstract Differential Equation of Fractional Order. Mathematical Notes, 2010, vol. 87, no. 5, pp. 654-662. https://doi.org/10.1134/S0001434610050056
2. Nakhushev A.M. Drobnoye ischisleniye i ego primeneniye [Fractional calculus and its applications]. Moscow, Fizmalit Publ., 2003, 272 p. (in Russian)
3. Pskhu A.V. Initial-value problem for a linear ordinary differential equation of noninteger order. Sbornik Mathematics, 2011, vol. 202, no. 4, pp. 571-582. http://dx.doi.org/10.1070/SM2011v202n04ABEH004156
4. Pyatkov S.G. Boundary Value and Inverse Problems for Some Classes of Nonclassical Operator-Differential Equations. Siberian Mathematical Journal, 2021, vol. 62, no. 3, pp. 489-502. https://doi.org/10.1134/S0037446621030125
5. Tikhonov I.V., Eidelman Yu.S. Problems on correctness of ordinary and inverse problems for evolutionary equations of a special form. Mathematical Notes, 1994, vol. 56, no. 2, pp. 830-839. https://doi.org/10.1007/BF02110743
6. Triebel H. Interpolation Theory. Function Spaces. Differential Operators. Berlin, VEB Deutscher Verlag der Wissenschaften, 1978, 531 p.
7. Falaleev M.V. Degenerated abstract problem of prediction-control in Banach spaces. The Bulletin of Irkutsk State University. Series Mathematics, 2010, vol. 3, pp. 126-132. (in Russian)
8. Fedorov V.E., Nagumanova A.V. Inverse Problem for Evolutionary Equation with the Gerasimov – Caputo Fractional Derivative in the Sectorial Case. The Bulletin of Irkutsk State University. Series Mathematics, 2019, vol. 28, pp. 123-137. https://doi.org/10.26516/1997-7670.2019.28.123 (in Russian)
9. Fedorov V.E., Kosti´c M. Identification Problem for Strongly Degenerate Evolution Equations with the Gerasimov – Caputo Derivative. Differential Equations, 2020, vol. 56, pp. 1613-1627. https://doi.org/10.1134/S00122661200120101
10. Fedorov V.E., Turov M.M. The Defect of a Cauchy Type Problem for Linear Equations with Several Riemann – Liouville Derivatives. Siberian Mathematical Journal,2021, vol. 62, no. 5, pp. 925-942. https://doi.org/10.1134/S0037446621050141
11. Al Horani M., Favini A. Degenerate first-order inverse problems in Banach spaces. Nonlinear Analysis, 2012, vol. 75, no. 1, pp. 68-77. https://doi.org/10.1016/j.na.2011.08.001
12. Fedorov V.E., Ivanova N.D. Identification problem for degenerate evolution equations of fractional order. Fractional Calculus and Applied Analysis, 2017, vol. 20, no. 3, pp. 706–721. https://doi.org/10.1515/fca-2017-0037
13. Fedorov V.E., Nagumanova A.V., Avilovich A.S. A class of inverse problems for evolution equations with the Riemann – Liouville derivative in the sectorial case. Mathematical Methods in the Applied Sciences, 2021, vol. 44, no. 15, pp. 11961-11969. https://doi.org/10.1002/mma.6794
14. Fedorov V.E., Nagumanova A.V., Kosti´c M. A class of inverse problems for fractional order degenerate evolution equations. Journal of Inverse and Ill-Posed Problems, 2021, vol. 29, no. 2, pp. 173-184. https://doi.org/10.1515/jiip-2017-0099
15. Hadid S.B., Luchko Yu.F. An operational method for solving fractional differential equations of an arbitrary real order. Panamerican Mathematical Journal, 1996, vol. 6, no. 1, pp. 57-73.
16. Jiang H., Liu F., Turner I., Burrage K. Analitical solutions for the multi-term time-space Caputo – Riesz fractional advection-diffussion equations on a finite domain. Journal of Mathematical Analysis and Applications, 2012, vol. 389, no. 2, pp. 1117-1127. https://doi.org/10.1016/j.jmaa.2011.12.055
17. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and Applications of Fractional Differential Equations. Amsterdam, Boston, Heidelberg,Elsevier Science Publ., 2006, 540 p.
18. Li C.-G., Kosti´c M., Li M. Abstract multi-term fractional differential equations. Kragujevac Journal of Mathematics, 2014, vol. 38, no. 1, pp. 51-71. https://doi.org/10.5937/KgJMath1401051L
19. Fedorov V.E., Kosti´c M. On a class of abstract degenerate multi-term fractional differential equations in locally convex spaces. Eurasian Mathematical Journal, 2018, vol. 9, no. 3, pp. 33-57. https://doi.org/10.32523/2077-9879-2018-9-3-33-57
20. Orlovsky D.G. Parameter determination in a differential equation of fractional order with Riemann – Liouville fractional derivative in a Hilbert space. Journal of Siberian Federal University. Mathematics & Physics, 2015, vol. 8, no. 1, pp. 55-63.
21. Prilepko A.I., Orlovskii D.G., Vasin I.A. Methods for Solving Inverse Problems in Mathematical Physics. New York, Basel, Marcel Dekker Inc., 2000, 744 p.
22. Sviridyuk G.A., Fedorov V.E. Linear Sobolev Type Equations and Degenerate Semigroups of Operators. Utrecht, Boston, VSP, 2003, 216 p.