In the present paper,we present some important properties of N-transform,which is the Laplace transform for the nabla derivative on the time scale of integers(Bohner and Peterson in Dynamic equations on time scales,Bi...In the present paper,we present some important properties of N-transform,which is the Laplace transform for the nabla derivative on the time scale of integers(Bohner and Peterson in Dynamic equations on time scales,Birkhauser,Boston,2001;Advances in dynamic equations on time scales,Birkhauser,Boston,2002).We obtain the N-transform of nabla fractional sums and differences and then apply this transform to solve some nabla fractional difference equations with initial value problems.Finally,usingN-transforms,we prove that discrete Mittag-Leffler function is the eigen function of Caputo type nabla fractional difference operator∇α.展开更多
文摘In the present paper,we present some important properties of N-transform,which is the Laplace transform for the nabla derivative on the time scale of integers(Bohner and Peterson in Dynamic equations on time scales,Birkhauser,Boston,2001;Advances in dynamic equations on time scales,Birkhauser,Boston,2002).We obtain the N-transform of nabla fractional sums and differences and then apply this transform to solve some nabla fractional difference equations with initial value problems.Finally,usingN-transforms,we prove that discrete Mittag-Leffler function is the eigen function of Caputo type nabla fractional difference operator∇α.
