Using the numerical solution for partial fractional differential equation by ADI numerical method to cryptography in Hill matrixes system

Abstract

Fractional calculus is the subject of evaluating derivatives and integrals of non-integer orders of a given function, fractional differential

equations is the subject of studying the solution of differential equations of fractional order is considered in this paper, which contain

initial conditions. The general form of a fractional differentia equation is given by:

y

(q)

 f(x, y), y(qk)(x0)  y0

where k  1, 2, …, n + 1, n < q < n + 1, and n is an integer number. The solution of fractional differential equations has so many

difficulties in their analytic solution, therefore numerical methods may be in most cases be the suitable method of solution.

Therefore, the objective of this paper is to introduce and study a numerical solution by ADI methods for solving fractional differential

equations.

Finally, we used the matrix optioned from this solution as a key matrix for cryptography the plaintext and transform it to cipher text by

using the method of Hill matrices system.