A numerical scheme for fractional order mortgage model of economics

Abstract

In this article, the famous mortgage model of economics is investigated by developing a numerical scheme. The considered model is proposed under the Caputo power law derivative of fractional order. Further, in the considered model by utilizing the time esteem of cash rule, we build up break even with vital and interest mortgage model that gives quickest installment plan with the least interest rate. The proposed scheme is based on some operational matrices of integration and differentiation of fractional order. For the required operational matrices, we use shifted Legendre polynomials. With the help of the operational matrices, we establish a numerical algorithm to convert the considered model to a system of Lyapunov matrix equation. By using Matlab, we then solve the resultant algebraic equation to get the required solution in numerical form. Further, we plot the approximate solution for various fractional order graphically.

Keywords

• Shifted Legendre polynomials
• Operational matrices
• Mortgage model
• Fractional-order differential equations