Geodesic
Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem
Archivum mathematicum, Tome 59 (2023) no. 1, pp. 117-123 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative.
We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative.
DOI : 10.5817/AM2023-1-117
Classification : 26A33, 34A08, 34K37
Keywords: Riemann-Liouville derivative; unique solvability; differential inequality 
@article{10_5817_AM2023_1_117,
     author = {Srivastava, Satyam Narayan and Domoshnitsky, Alexander and Padhi, Seshadev and Raichik, Vladimir},
     title = {Unique solvability of fractional functional differential equation on the basis of {Vall\'ee-Poussin} theorem},
     journal = {Archivum mathematicum},
     pages = {117--123},
     year = {2023},
     volume = {59},
     number = {1},
     doi = {10.5817/AM2023-1-117},
     mrnumber = {4563022},
     zbl = {07675580},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-117/}
}
TY  - JOUR
AU  - Srivastava, Satyam Narayan
AU  - Domoshnitsky, Alexander
AU  - Padhi, Seshadev
AU  - Raichik, Vladimir
TI  - Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem
JO  - Archivum mathematicum
PY  - 2023
SP  - 117
EP  - 123
VL  - 59
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-117/
DO  - 10.5817/AM2023-1-117
LA  - en
ID  - 10_5817_AM2023_1_117
ER  - 
%0 Journal Article
%A Srivastava, Satyam Narayan
%A Domoshnitsky, Alexander
%A Padhi, Seshadev
%A Raichik, Vladimir
%T Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem
%J Archivum mathematicum
%D 2023
%P 117-123
%V 59
%N 1
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2023-1-117/
%R 10.5817/AM2023-1-117
%G en
%F 10_5817_AM2023_1_117
Srivastava, Satyam Narayan; Domoshnitsky, Alexander; Padhi, Seshadev; Raichik, Vladimir. Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem. Archivum mathematicum, Tome 59 (2023) no. 1, pp. 117-123. doi: 10.5817/AM2023-1-117

[1] Agarwal, R.P., Bohner, M., Özbekler, A.: Lyapunov Inequalities and Applications. Springer, Berlin, 2021. | MR

[2] Azbelev, N.V., Maksimov, V.P., Rakhmatullina, L.F.: Introduction to the Theory of Functional Differential Equations. Hindawi Publishing, 2007. | MR

[3] Benmezai, A., Saadi, A.: Existence of positive solutions for a nonlinear fractional differential equations with integral boundary conditions. J. Fract. Calc. Appl. 7 (2) (2016), 145–152. | MR

[4] Domoshnitsky, A., Padhi, S., Srivastava, S.N.: Vallée-Poussin theorem for fractional functional differential equations. Fract. Calc. Appl. Anal. 25 (2022), 1630–1650, | DOI | MR

[5] Ferreira, R.: A Lyapunov-type inequality for a fractional boundary value problem. Fract. Calc. Appl. Anal. 16 (4) (2013), 978–984, | DOI | MR

[6] Ferreira, R.A.: Existence and uniqueness of solutions for two-point fractional boundary value problems. Electron. J. Differential Equations 202 (5) (2016). | MR

[7] Henderson, J., Luca, R.: Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions. Academic Press, 2015. | MR

[8] Henderson, J., Luca, R.: Nonexistence of positive solutions for a system of coupled fractional boundary value problems. Bound. Value Probl. 2015 (1) (2015), 1–12. | MR

[9] Henderson, J., Luca, R.: Positive solutions for a system of semipositone coupled fractional boundary value problems. Bound. Value Probl. 2016 (1) (2016), 1–23. | MR

[10] Jankowski, T.: Positive solutions to fractional differential equations involving Stieltjes integral conditions. Appl. Math. Comput. 241 (2014), 200–213. | DOI | MR

[11] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, 2006. | MR | Zbl

[12] Krasnosel’skii, M.A., Vainikko, G.M., Zabreyko, R.P., Ruticki, Y.B., Stet’senko, V.V.: Approximate Solution of Operator Equations. Springer Science & Business Media, 2012.

[13] Padhi, S., Graef, J.R., Pati, S.: Multiple positive solutions for a boundary value problem with nonlinear nonlocal Riemann-Stieltjes integral boundary conditions. Fract. Calc. Appl. Anal. 21 (3) (2018), 716–745, | DOI | MR

[14] Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego, 1999. | Zbl

[15] Qiao, Y., Zhou, Z.: Existence of positive solutions of singular fractional differential equations with infinite-point boundary conditions. Adv. Difference Equations 2017 (1) (2017), 1–9. | MR

Cité par Sources :