Faculty of Mathematics and Computer Science
University of Lodz
Banacha 22 90-238 Lodz, Poland
email: dariusz.idczak@wmii.uni.lodz.pl
Dariusz Idczak
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.
Submitted April 11, 2026. Published July 24, 2026.
Math Subject Classifications: 35R11, 35G31, 35C15, 35A01, 35A02, 35D35.
Key Words: Riemann-Liouville derivative; fractional partial differential equation; integral equation;
Schaefer fixed point theorem; Gronwall lemma.
DOI: 10.58997/ejde.2026.57
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Dariusz Idczak Faculty of Mathematics and Computer Science University of Lodz Banacha 22 90-238 Lodz, Poland email: dariusz.idczak@wmii.uni.lodz.pl |
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