This paper presents (p, q)-analogues of the \(\alpha \) -th fractional Fourier transform and discusses their properties on a certain class of (p, q)-generalized functions. By introducing two (p, q)-differential operators, distributional and generalized distributional spaces of (p, q)-Boehmians are obtained. Consequently, the (p, q)-analogues of the \(\alpha \) -th fractional Fourier transform are shown to be linear and continuous between the considered spaces. Further theorems associated with certain (p, q)-convolutions are then proved. Moreover, multiple identities and properties of the generalized spaces of distributions and the so-called (p, q)-Boehmians are discussed in a generalized sense. Moreover, the generalized \(\alpha \) -th (p, q)-fractional Fourier transform and its general features, along with derivation of inversion formulas, are addressed.
