Generalized fractional Clairaut equation in infinite-dimensional spaces
Year: 2026
Type: article
Abstract: This paper introduces and studies a generalized fractional Clairaut differential equation ( GFCDE ) within the framework of Wick calculus over spaces of generalized functions. As a foundational step, we extend the modified Mittag-Leffler function to act on generalized functions. Using this extension, we establish that the explicit solution of the Atangana–Baleanu Caputo (ABC) GFCDE is given by the Wick product of the initial condition and a fundamental solution, where the latter is formulated as a generalized process involving the modified Mittag-Leffler function. Finally, we demonstrate that the solution admits an integral representation, characterized by a unique positive Radon measure.
Authors: Amine Ettaieb, Hafedh Rguigui
Institution: University of Sousse
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,390
OpenAlex ID: W7155899681