Wave equations for the fractional Sturm-Liouville operator with singular coefficients

Ruzhansky M. Sebih M.E. Yeskermessuly A.
2025 University of Nis

Filomat
2025 #39 Issue 35 12555 - 12579 pp.

In this paper, we consider the wave equation for the fractional Sturm-Liouville operator with lower order terms and singular coefficients and data. We prove that the problem has a very weak solution. Furthermore, we prove the uniqueness in an appropriate sense and the consistency of the very weak solution concept with the classical theory.

energy methods , fractional Sturm-Liouville operator , initial/boundary problem , position dependent coefficients , regularisation , separation of variables , singular coefficients , very weak solution , wave equation , weak solution

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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Building S8, Ghent, 9000, Belgium
School of Mathematical Sciences, Queen Mary University of London, London, United Kingdom
Laboratory of Geomatics, Ecology and Environment (LGEO2E), University Mustapha Stambouli of Mascara, Mascara, 29000, Algeria
Faculty of Natural Sciences and Informatization, Altynsarin University, Auelbekov, 17, Arkalyk, P10A1P9, Kazakhstan

Department of Mathematics: Analysis
School of Mathematical Sciences
Laboratory of Geomatics
Faculty of Natural Sciences and Informatization

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