| Title:
|
General exact solvability conditions for the initial value problems for linear fractional functional differential equations (English) |
| Author:
|
Dilna, Natalia |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
59 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
11-19 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Conditions on the unique solvability of linear fractional functional differential equations are established. A pantograph-type model from electrodynamics is studied. (English) |
| Keyword:
|
fractional order functional differential equations |
| Keyword:
|
Caputo derivative |
| Keyword:
|
normal and reproducing cone |
| Keyword:
|
unique solvability |
| MSC:
|
26A33 |
| MSC:
|
34A08 |
| MSC:
|
34B15 |
| idZBL:
|
Zbl 07675570 |
| idMR:
|
MR4563012 |
| DOI:
|
10.5817/AM2023-1-11 |
| . |
| Date available:
|
2023-02-22T14:20:28Z |
| Last updated:
|
2023-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151546 |
| . |
| Reference:
|
[1] Aphithana, A., Ntouyas, S.K., Tariboon, J.: Existence and uniqueness of symmetric solutions for fractional differential equations with multi-point fractional integral conditions.Bound. Value Probl. 2015 (68) (2015), 14 pp., https://doi.org/10.1186/s13661-015-0329-1. MR 3338722, 10.1186/s13661-015-0329-1 |
| Reference:
|
[2] Diethelm, K.: The Analysis of Fractional Differential Equations. An Application-Oriented Exposition Using Differential Operators of Caputo Type.Springer, 2010. Zbl 1215.34001, MR 2680847 |
| Reference:
|
[3] Dilna, N.: Exact solvability conditions for the model with a discrete memory effect.International Conference on Mathematical Analysis and Applications in Science and Engineering, Book of Extended Abstracts, 2022, 405–407 pp. |
| Reference:
|
[4] Dilna, N., Fečkan, M.: Exact solvability conditions for the non-local initial value problem for systems of linear fractional functional differential equations.Mathematics 10 (10) (2022), 1759, https://doi.org/10.3390/math10101759. MR 4563012, 10.3390/math10101759 |
| Reference:
|
[5] Dilna, N., Gromyak, M., Leshchuk, S.: Unique solvability of the boundary value problems for nonlinear fractional functional differential equations.J. Math. Sci. 265 (2022), 577–588, https://doi.org/10.1007/s10958-022-06072-8. MR 4518887, 10.1007/s10958-022-06072-8 |
| Reference:
|
[6] Fečkan, M., Marynets, K.: Approximation approach to periodic BVP for fractional differential systems.The European Physical Journal Special Topics 226 (2017), 3681–3692, https://doi.org/10.1140/epjst/e2018-00017-9. 10.1140/epjst/e2018-00017-9 |
| Reference:
|
[7] Fečkan, M., Wang, J.R., Pospíšil, M.: Fractional-Order Equations and Inclusions.1st. ed., Walter de Gruyter GmbH, Berlin, Boston, 2017. |
| Reference:
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[8] Gautam, G.R., Dabas, J.: A study on existence of solutions for fractional functional differential equations.Collect. Math 69 (2018), 25–37. MR 3742978, 10.1007/s13348-016-0189-8 |
| Reference:
|
[9] Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations.Elsevier B.P., 2006. Zbl 1092.45003, MR 2218073 |
| Reference:
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[10] Opluštil, Z.: New solvability conditions for a non-local boundary value problem for nonlinear functional-differential equations.Nonlinear Oscil. 11 (3) (2008), 365–386. MR 2512754, 10.1007/s11072-009-0038-8 |
| Reference:
|
[11] Patade, J., Bhalekar, S.: Analytical solution of pantograph equation with incommensurate delay.Phys. Sci. Rev. Inform. 9 (2017), 20165103 https://doi.org/10.1515/psr-2016-5103. 10.1515/psr-2016-5103 |
| Reference:
|
[12] Reed, M., Simon, B.: Methods of modern mathematical physics.Acad. Press, New York-London, 1972. |
| Reference:
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[13] Rontó, A., Rontó, M.: Successive Approximation Techniques in Non-Linear Boundary Value Problems.Handbook of Differential Equations: Ordinary Differential Equations, Elsevier, New York, 2009, pp. 441–592. MR 2440165 |
| Reference:
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[14] Šremr, J.: Solvability conditions of the Cauchy problem for two-dimensional systems of linear functional differential equations with monotone operators.Math. Bohem. 132 (2007), 263–295. MR 2355659, 10.21136/MB.2007.134126 |
| . |
