NEW DEFINITION OF N_F^α-LAPLACE CONFORMABLE TRANSFORM AND THEIR APPLICATIONS

Abstract

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