The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer orderμ∈(1,2].The required conditions are obtained by appl...The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer orderμ∈(1,2].The required conditions are obtained by applying the technique of contraction principle for uniqueness and Schauder’s fixed point theorem for existence.Also,we establish some conditions under which the solution of the considered class of difference equations is generalized Ulam-Hyers-Rassias stable.Example for the illustration of results is given.展开更多
This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational ...This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.展开更多
文摘The purpose of this study is to acquire some conditions that reveal existence and stability for solutions to a class of difference equations with non-integer orderμ∈(1,2].The required conditions are obtained by applying the technique of contraction principle for uniqueness and Schauder’s fixed point theorem for existence.Also,we establish some conditions under which the solution of the considered class of difference equations is generalized Ulam-Hyers-Rassias stable.Example for the illustration of results is given.
文摘This paper mainly discusses the problems of fractional variational problems and fractional diffusion problems using fractional difference and summation. Through the Euler finite difference method we get a variational formulation of the variation problem and the discrete solution to the time-fractional and space-fractional difference equation using separating variables method and two-side Z-transform method.
