M.Sc.

In this thesis, we introduce a modified approach for solving fractional order boundary value problems. This approach is given by applying the Riesz-Feller operator to obtain a modified finite difference equation, which is symmetric to the equation of fractional boundary value problems. Also, the main objective of this work is to study the existence and uniqueness theorem of solutions of the fractional boundary value problems, and to present their proof depending on Schauder fixed point theorem for fractional order integral operator.