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

Abstract

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 supported by:

y^(s) = k(c, u), y^(stk) (c₀) = u.

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.

This paper introduces and study a numerical solution by ADI methods for solving fractional differential equations.

We used the matrix obtained from this solution as a key matrix for cryptography the plain text and transform it to cipher text by using the method of Hill matrix system the quantity demand and investment in research and development, while the other model focuses on a more realistic relationship between the quantity demand and the price.

Subject Classification:

• 11T71
• 94A60

Keywords:

• Fractional partial differential equations
• ADI methods
• Hill matrix
• Cryptography