Some results of new definition of N_F^α-Fourier transform and their applications

Based on a new definition of fractional derivative, called NFα-derivative, we introduce a new definition and present some results on NαF-periodic functions and NFα-Fourier transform related to this type of functions. We also use these results to study the NFα-partial differential equation NFαx(t) = A x(t) + IFαx(t) + f(t), where A is a linear closed operator on a Banach space X.