New Definition of N α F -Sumudu conformable transform

Abstract

Using the new definition of the $\mathcal{N}^{\alpha}_F$-derivative function introduced by Juan E. Nápoles Valdés and al. (2020), we provide a new definition for the $\mathcal{N}^{\alpha}_F$-Sumudu transform, $\mathcal{N}^{\alpha}_F$-Sumudu conformable transform. Additionally, we establish several important results related to these new transforms. We also give a new definition of convolution related to this $\mathcal{N}^{\alpha}_F$-derivative and we show that it is commutative and associative.