All of us who had studied Mathematics at college/university knows about Laplace Transform and Fourier Transform, and in some institutions Z transform is also taught.
Researchers also introduced different transforms like: Sumudu transform, N transform, Differential transform, Aboodh transform, complex transform…etc. As far as I have studied these transforms I haven't seen clear difference. Moreover one integral transform can be expressed in other transform.
At this time researchers may be also trying to introduce new integral transform. My questions come here, why to introduce new transform? Why/when we will use the above listed integral transforms?
For better accuracy and conversion speed with different frequency signals with half or full window width...
Each integral transform is introduced based on purpose and each is expected to have a limited application coverage. For instance, while, Fourier transform maps a function from real to complex domain (transforming a function from time domain to frequency domain in signal processing usage) it is also called the complex function of a real variable; the Laplace transform also maps a function from real to complex domain and is somewhat similar to Fourier transform especially when the real part equates zero, so, it is also called complex function of a complex variable. Both Fourier and Laplace transforms are used for continuous functions. However, both cannot be used for discrete functions. Meanwhile, a lot of applications are now based on discrete systems, hence, the need for a discrete integral transform such as Z-transform and its likes, with each having its pros and cons. So in brevity, the needs in various applications give rise to the development of new integral transforms and understanding your need determines what to use when.
Different transformations (not just integral ones) may have distinguished convenience at realization and analyze. Their application for different ranges of variables may by accompanied with differed calculative errors or deviations that can be important for some special cases. Besides, sometimes (but rarely) some transformation can have physical meaning and interpretation.