Geodesic
Correct solvability of problems for fractional-power operator equations
Contemporary Mathematics. Fundamental Directions, Proceedings of the Voronezh Winter Mathematical Krein School — 2024, Tome 70 (2024) no. 4, pp. 533-541 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, we consider the sum of linear fractional-power operators acting in a Banach space and satisfying weak positivity. We establish the correct solvability of the problem for the corresponding fractional-operator equation and we give the representation of the solution through the inverse operator with an exact estimate of its norm. The results are applied to problems without initial conditions for an equation with singular coefficients. We consider examples of such equations.
Keywords: fractional power operator, fractional-operator equation, correct solvability. 
@article{CMFD_2024_70_4_a1,
     author = {S. D. Baboshin},
     title = {Correct solvability of problems for fractional-power operator equations},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {533--541},
     year = {2024},
     volume = {70},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2024_70_4_a1/}
}
TY  - JOUR
AU  - S. D. Baboshin
TI  - Correct solvability of problems for fractional-power operator equations
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2024
SP  - 533
EP  - 541
VL  - 70
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/CMFD_2024_70_4_a1/
LA  - ru
ID  - CMFD_2024_70_4_a1
ER  - 
%0 Journal Article
%A S. D. Baboshin
%T Correct solvability of problems for fractional-power operator equations
%J Contemporary Mathematics. Fundamental Directions
%D 2024
%P 533-541
%V 70
%N 4
%U http://geodesic.mathdoc.fr/item/CMFD_2024_70_4_a1/
%G ru
%F CMFD_2024_70_4_a1
S. D. Baboshin. Correct solvability of problems for fractional-power operator equations. Contemporary Mathematics. Fundamental Directions, Proceedings of the Voronezh Winter Mathematical Krein School — 2024, Tome 70 (2024) no. 4, pp. 533-541. http://geodesic.mathdoc.fr/item/CMFD_2024_70_4_a1/

[1] K. Yosida, Functional Analysis, Russian translation, Mir, M., 1967 | MR

[2] V. A. Kostin, A. V. Kostin, and D. V. Kostin, “Elementary semigroups of transformations and their generating equations”, Rep. Russ. Acad. Sci., 455:2 (2014), 142–146 (in Russian) | DOI | Zbl

[3] S. G. Kreyn, Linear Differential Equations in a Banach space, Nauka, M., 1967 (in Russian)

[4] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications, Nauka i Tekhnika, Minsk, 1987 (in Russian)

[5] A. N. Tikhonov, Equations of Mathematical Physics, Nauka, M., 1966 (in Russian) | MR

[6] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Russian translation, Inostr. Lit., M., 1962 | MR

[7] Da Prato G., Grisvard P., “Sommes d'opérateurs linéaires et équations différentielles opérationnelles”, J. Math. Pures Appl. (9), 54 (1975), 305–387 | MR | Zbl

[8] Hilfer R., “Threefold introduction to fractional derivatives”, Anomalous Transport: Foundations and Applications, Wiley-VCH, Weinheim, 2008, 17–73 | DOI

[9] Kolokoltsov V. N., Shishkina E. L., “Fractional calculus for non-discrete signed measures”, Mathematics, 12 (2024), 2804 | DOI