On the fractional Laplacian of a function with respect to another function
Fernandez A. Restrepo J.E. Djida J.-D.
December 2024John Wiley and Sons Ltd
Mathematical Methods in the Applied Sciences
2024#47Issue 1814079 - 14110 pp.
The theories of fractional Laplacians and of fractional calculus with respect to functions are combined to produce, for the first time, the concept of a fractional Laplacian with respect to a bijective function. The theory is developed both in the 1-dimensional setting and in the general (Formula presented.) -dimensional setting. Fourier transforms with respect to functions are also defined, and the relationships between Fourier transforms, fractional Laplacians, and Marchaud-type derivatives are explored. Function spaces for these operators are carefully defined, including weighted (Formula presented.) spaces and a new type of Schwartz space. The theory developed is then applied to construct solutions to some partial differential equations involving both fractional time derivatives and fractional Laplacians with respect to functions, with illustrative examples.
fractional calculus with respect to functions , fractional Laplacian , fractional partial differential equations , weighted Lp$$ {L}^p $$ spaces
Text of the article Перейти на текст статьи
Department of Mathematics, Eastern Mediterranean University, Northern Cyprus, Famagusta, Turkey
Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Ghent, Belgium
Department of Mathematics, Nazarbayev University, Astana, Kazakhstan
Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
Department of Mathematics
Department of Mathematics: Analysis
Department of Mathematics
Department of Mathematics
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026