Abstract
Based on a new definition of $\alpha$-periodical functions with $0 < \alpha \leq 1$ introduced by Khalil et al. (2014), we introduce a new definition of conformable Fourier transform for such a class of functions. Further, we establish some operational formulas, and we set the relation between the newly defined conformable Fourier transform and the classical Fourier transform. Finally, some classical results of periodical functions are obtained, and some illustrative examples are constructed.
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