Received January 5, 2025. Published online February 18, 2026.
Abstract: We study a fractional parabolic problem with a variable exponent and an integrable source term. Our goal is to establish the existence and uniqueness of a renormalized solution. The functional setting involves Lebesgue and Sobolev spaces with variable exponent. Some a-priori estimates are used to obtain our results.
Keywords: fractional $p({\cdot})$-Laplacian; parabolic problem; existence and uniqueness of renormalized solution; variable exponent
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Affiliations: Salifou Korbeogo (corresponding author), Arouna Ouedraogo, Laboratoire de Mathématiques, Informatique et Applications, Université Norbert Zongo, BP 376 Koudougou, Burkina Faso, e-mail: salifoukorbeogo.73@gmail.com; Frédéric D. Y. Zongo, Laboratoire Interdisciplinaire de Recherche en Sciences Appliquées (LIRSA), École Normale Supérieure, 01 BP 1757 Ouagadougou 01, Burkina Faso
