@ARTICLE{10.21494/ISTE.OP.2023.0998, 

TITLE={Weyl almost automorphic functions and applications}, 
  
AUTHOR={M. Kostić, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={14}, 

NUMBER={Issue 4 (September 2023)}, 
	
YEAR={2023}, 

URL={https://openscience.fr/Weyl-almost-automorphic-functions-and-applications}, 
	
DOI={10.21494/ISTE.OP.2023.0998}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={In this paper, we reconsider the notion of a Weyl p-almost automorphic function introduced by S. Abbas [1] in 2012 and propose several new ways for introduction of the class of Weyl p-almost automorphic functions (1 ⩽ p < ∞). We first analyze the introduced classes of Weyl p-almost automorphic functions of type 1, jointly Weyl p-almost automorphic functions and Weyl p-almost automorphic functions of type 2 in the one-dimensional setting. After that, we introduce and analyze generalizations of these classes in the multi-dimensional setting, working with general Lebesgue spaces with variable exponents. We provide several illustrative examples and applications to the abstract Volterra integro-differential equations.}}