M.Sc.

  Alternating Direction Implicit method (ADI) was first suggested by Peaceman and Rachford in the mid-50s of the last century for solving systemsb of algebraic equations in two dimension of  aces[peaceman and rachford,1955], which results from the finite difference discretization method for solving PDEs; [Peaceman and Rachford,1955].

      The main theme of this thesis is to study and find the numerical solution of fractional order delay differential equations, and may be divided into two sub objectives, as follows:

The generalization of metric spaces from ordinary sets to fuzzy set theoryand then to the so called cone metric spaces is a promising topics of theoreticalmathematics.