Using the numerical solution for partial fractional differential equation by ADI numerical method to cryptography in Hill matrixes system
الملخص
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(qk)(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.
