A Numerical solution for the new model of time-fractional bond pricing‎: ‎Using a multiquadric approximation method

‎The bond market is an important part of the financial markets‎ . ‎The coupon bonds are issued by companies or banks for increasing capital ‎, ‎and the interest is paid by banks or companies‎, ‎periodically ‎.‎ ‎In terms of maturities ‎, ‎bonds are divided into three categories as follows‎ : ‎short term‎ , ‎medium term‎ , ‎and long ‎term‎ .‎‎In this paper‎ , ‎we model the fractional bond pricing under fractional stochastic differential equation ‎. ‎We implement the multiquadric approximation for solving the fractional bond pricing equation‎ . ‎The equation is discretized in the time direction base on modified Riemann-- Liouville derivative and finite difference methods and is approximated by using the multiquadric approximation method in the space direction which achives the semi-- discrete solution‎ . ‎We investigate the unconditional stability and convergence of the proposed method‎. ‎Numerical results demonstrate the efficiency and ability of the presented method ‎.