Abstract
This paper primarily lies in presenting existence and uniqueness analysis of boundary fractional difference equations of a special Riemann–Liouville operators classes. To this end, we first develop Green’s function to the corresponding fractional boundary value problems and provide boundary conditions to find the constants. Then we study the existence of solutions and we examine the bounded of their solutions. Eventually, two numerical examples are given to demonstrate the efficiency and uniqueness behavior of the boundary value problem. Furthermore, such fractional problems can typically be converted to a direct fractional problem with certain boundary or initial conditions in transport in porous media.
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