On the structural properties of Fm-transform with applications

The aim of this study is to obtain some direct formulas for Fm-transforms of derivative, integral and multiplication of functions in order to extend the application and flexibility of Fm-transform method. Using the derived explicit formula, one can use Fm-transform method straightforwardly to solve various linear and nonlinear problems including differential and integral equations. In this study, the general form of the higher order fuzzy transforms are constructed using any arbitrary basis functions instead of the classical polynomial ones.