Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem

Satyam Narayan Srivastava; Alexander Domoshnitsky; Seshadev Padhi; Vladimir Raichik

Archivum Mathematicum (2023)

  • Issue: 1, page 117-123
  • ISSN: 0044-8753

Abstract

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We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative.

How to cite

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Srivastava, Satyam Narayan, et al. "Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem." Archivum Mathematicum (2023): 117-123. <http://eudml.org/doc/298981>.

@article{Srivastava2023,
abstract = {We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative.},
author = {Srivastava, Satyam Narayan, Domoshnitsky, Alexander, Padhi, Seshadev, Raichik, Vladimir},
journal = {Archivum Mathematicum},
keywords = {Riemann-Liouville derivative; unique solvability; differential inequality},
language = {eng},
number = {1},
pages = {117-123},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Unique solvability of fractional functional differential equation on the basis of Vallée-Poussin theorem},
url = {http://eudml.org/doc/298981},
year = {2023},
}

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
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
IS - 1
SP - 117
EP - 123
AB - We propose explicit tests of unique solvability of two-point and focal boundary value problems for fractional functional differential equations with Riemann-Liouville derivative.
LA - eng
KW - Riemann-Liouville derivative; unique solvability; differential inequality
UR - http://eudml.org/doc/298981
ER -

References

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  2. Azbelev, N.V., Maksimov, V.P., Rakhmatullina, L.F., Introduction to the Theory of Functional Differential Equations, Hindawi Publishing, 2007. (2007) MR2319815
  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. (2016) MR3481772
  4. Domoshnitsky, A., Padhi, S., Srivastava, S.N., 10.1007/s13540-022-00061-z, Fract. Calc. Appl. Anal. 25 (2022), 1630–1650, https://doi.org/10.1007/s13540-022-00061-z. (2022) MR4468528DOI10.1007/s13540-022-00061-z
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  6. Ferreira, R.A., Existence and uniqueness of solutions for two-point fractional boundary value problems, Electron. J. Differential Equations 202 (5) (2016). (2016) MR3547391
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  11. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J., Theory and Applications of Fractional Differential Equations, Elsevier, 2006. (2006) Zbl1092.45003MR2218073
  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. (2012) 
  13. Padhi, S., Graef, J.R., Pati, S., 10.1515/fca-2018-0038, Fract. Calc. Appl. Anal. 21 (3) (2018), 716–745, https://doi.org/10.1515/fca-2018-0038. (2018) MR3827151DOI10.1515/fca-2018-0038
  14. Podlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999. (1999) Zbl0924.34008
  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. (2017) MR3594502

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