Inversion Theorem of Fractional Sumudu–Fourier Transform

Abstract

The Fractional Sumudu–Fourier Transform (FrSFT) is a useful integral transform that combines the important features of the Sumudu Transform and the Fractional Fourier Transform. It provides an effective approach for studying functions with fractional and oscillatory behaviour and has potential applications in mathematics, signal processing, and engineering. An inversion theorem is an essential property of any integral transform because it guarantees that the original function can be recovered from its transformed form. In this work, the inversion theorem for the Fractional Sumudu–Fourier Transform is established using testing function spaces and generalized functions. The obtained result confirms the mathematical validity of the transform and provides a foundation for its future applications in both theoretical and applied mathematics.