Geodesic
An inverse problem for a class of degenerate evolution multi-term equations with Gerasimov--Caputo derivatives
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 38-46.

Voir la notice de l'article provenant de la source Math-Net.Ru

Issues of well-posedness of linear inverse problems for equations with several Gerasimov–Caputo fractional derivatives in Banach spaces are investigated. The inverse coefficient problem is considered for an equation solved with respect to the highest fractional derivative containing bounded operators at lower order derivatives. The criterion of well-posedness of such a problem is proved. A similar inverse problem for an equation with a degenerate operator at the highest derivative, assuming the relative 0-boundedness of a pair of operators at two higher derivatives, is reduced to two problems on subspaces for equations solved with respect to the highest derivative. The obtained well-posedness criteria allowed us to investigate one class of inverse problems for equations with polynomials from an elliptic differential operator with respect to spatial variables and with several Gerasimov–Caputo time derivatives.
Keywords: Gerasimov–Caputo fractional derivative, degenerate evolution equation, problem well-posedness.
Mots-clés : inverse coefficient problem 
@article{INTO_2022_213_a2,
     author = {K. V. Boyko and V. E. Fedorov},
     title = {An inverse problem for a class of degenerate evolution multi-term equations with {Gerasimov--Caputo} derivatives},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {38--46},
     publisher = {mathdoc},
     volume = {213},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_213_a2/}
}
TY  - JOUR
AU  - K. V. Boyko
AU  - V. E. Fedorov
TI  - An inverse problem for a class of degenerate evolution multi-term equations with Gerasimov--Caputo derivatives
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 38
EP  - 46
VL  - 213
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_213_a2/
LA  - ru
ID  - INTO_2022_213_a2
ER  - 
%0 Journal Article
%A K. V. Boyko
%A V. E. Fedorov
%T An inverse problem for a class of degenerate evolution multi-term equations with Gerasimov--Caputo derivatives
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 38-46
%V 213
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_213_a2/
%G ru
%F INTO_2022_213_a2
K. V. Boyko; V. E. Fedorov. An inverse problem for a class of degenerate evolution multi-term equations with Gerasimov--Caputo derivatives. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Geometry, Mechanics, and Differential Equations, Tome 213 (2022), pp. 38-46. http://geodesic.mathdoc.fr/item/INTO_2022_213_a2/

[1] Glushak A. V., “Zadacha tipa Koshi dlya abstraktnogo differentsialnogo uravneniya s drobnymi proizvodnymi”, Mat. zametki., 77:1 (2005), 28–41 | DOI | MR | Zbl

[2] Glushak A. V., “Obratnaya zadacha dlya abstraktnogo differentsialnogo uravneniya Eilera—Puassona—Darbu”, Sovr. mat. Fundam. napr., 15 (2006), 126–141

[3] Glushak A. V., “Ob odnoi obratnoi zadache dlya abstraktnogo differentsialnogo uravneniya drobnogo poryadka”, Mat. zametki., 87:5 (2010), 684–693 | DOI | MR | Zbl

[4] Tribel Kh., Teoriya interpolyatsii. Funktsionalnye prostranstva. Differentsialnye operatory, Mir, M., 1980

[5] Fedorov V. E., “Silno golomorfnye gruppy lineinykh uravnenii sobolevskogo tipa v lokalno vypuklykh prostranstvakh”, Differ. uravn., 40:5 (2004), 702–712 | DOI | MR | Zbl

[6] Fedorov V. E., Boiko K. V., Fuong T. D., “Nachalnye zadachi dlya nekotorykh klassov lineinykh evolyutsionnykh uravnenii s neskolkimi drobnymi proizvodnymi”, Mat. zametki SVFU., 28:3 (2021), 85–104 | DOI

[7] Fedorov V. E., Turov M. M., “Defekt zadachi tipa Koshi dlya lineinykh uravnenii s neskolkimi proizvodnymi Rimana—Liuvillya”, Sib. mat. zh., 62:5 (2021), 1143–1162 | DOI | Zbl

[8] Alvarez-Pardo E., Lizama C., “Mild solutions for multi-term time-fractional differential equations with nonlocal initial conditions”, Electron. J. Differ. Equations., 2014:39 (2014), 1–10 | MR

[9] Fedorov V. E., Kostić M., “On a class of abstract degenerate multi-term fractional differential equations in locally convex spaces”, Euras. Math. J., 9:3 (2018), 33–57 | DOI | MR | Zbl

[10] Fedorov V. E., Nagumanova A. V., Kostić M., “A class of inverse problems for fractional order degenerate evolution equations”, J. Inv. Ill-Posed Probl., 29:2 (2020), 173–184 | DOI | MR

[11] 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”, J. Math. Anal. Appl., 389:2 (2012), 1117–1127 | DOI | MR | Zbl

[12] Li C.-G., Kostic̀ M., Li M., “Abstract multi-term fractional differential equations”, Kragujevac J. Math., 38:1 (2014), 51–71 | DOI | MR | Zbl

[13] Liu F., Meerschaert M. M., McGough R. J., Zhuang P., Liu Q., “Numerical methods for solving the multi-term time-fractional wave-diffusion equation”, Fract. Calc. Appl. Anal., 16:1 (2013), 9–25 | DOI | MR | Zbl

[14] Lizama C., Prado H., “Fractional relaxation equations on Banach spaces”, Appl. Math. Lett., 23:1 (2010), 137–142 | DOI | MR | Zbl

[15] Orlovsky D. G., “Parameter determination in a differential equation of fractional order with Riemann–Liouville fractional derivative in a Hilbert space”, Zh. SFU. Ser. Mat. Fiz., 8:1 (2015), 55–63 | MR | Zbl

[16] Sviridyuk G. A., Fedorov V. E., Linear Sobolev type equations and degenerate semigroups of operators, VSP, Utrecht, Boston, 2003 | MR | Zbl