In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fraction...In this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fractional calculus approach is used in the governing equations. The exact solutions are established by means of the Fourier sine transform and N-transform. The series solutions of velocity field and associated shear stress in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. The similar solutions for ordinary Jeffrey fluid, performing the same motion, appear as limiting case of the solutions are also obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.展开更多
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 this paper, we presents some new exact solutions corresponding to three unsteady flow problems of a generalized Jeffrey fluid produced by a flat plate between two side walls perpendicular to the plate. The fractional calculus approach is used in the governing equations. The exact solutions are established by means of the Fourier sine transform and N-transform. The series solutions of velocity field and associated shear stress in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. The similar solutions for ordinary Jeffrey fluid, performing the same motion, appear as limiting case of the solutions are also obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.
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.
