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Peer-reviewedCC BYElectronic Journal of Differential Equations

Fractional multiterm Gronwall lemma for functions of two variables and its application to fractional higher-order systems of hyperbolic type

  • Dariusz Idczak1
  1. 1Univ. of Lodz, Poland
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Abstract

We study a fractional (in Riemann-Liouville sense) partial differential problem of higher order in the space of fractionally absolutely continuous functions of two variables. We obtain existence of a solution in a non-Lipschitz case applying the Schaeffer fixed point theorem and a fractional multiterm Gronwall lemma for functions of two variables to a nonlinear integral equation.

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Cite

BibTeXRIS
BibTeX
@article{idczak2026fractional,
  title = {{Fractional multiterm Gronwall lemma for functions of two variables and its application to fractional higher-order systems of hyperbolic type}},
  author = {Dariusz Idczak},
  journal = {Electronic Journal of Differential Equations},
  year = {2026},
  month = jul,
  url = {http://ejde.math.txstate.edu/Volumes/2026/57/abstr.html},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Fractional multiterm Gronwall lemma for functions of two variables and its application to fractional higher-order systems of hyperbolic type
AU  - Dariusz Idczak
PY  - 2026
DA  - 2026/07/01
JO  - Electronic Journal of Differential Equations
UR  - http://ejde.math.txstate.edu/Volumes/2026/57/abstr.html
AB  - We study a fractional (in Riemann-Liouville sense) partial differential problem of higher order in the space of fractionally absolutely continuous functions of two variables. We obtain existence of a solution in a non-Lipschitz case applying the Schaeffer fixed point theorem and a fractional multiterm Gronwall lemma for functions of two variables to a nonlinear integral equation.
SN  - 1072-6691
ER  -