Rajshree Mishra

The real-life problems related to engineering and physical systems are theoretically studied using mathematical models and are generally formulated using linear and nonlinear differential equations. This work proposes a numerical technique to find approximate solutions of differential equations utilizing polynomials as base approximation functions and metaheuristic optimization algorithms like differential evolution (DE) and particle swarm optimization (PSO) for obtaining the optimal values of coefficients of the polynomials in order to get the desired approximate solution. The algorithms for the proposed method have been executed using MATLAB for computer programming. The effectiveness of the approach presented in this paper is found to be better than or at least comparable to other numerical methods suggested earlier for solving differential equations.

The main purpose of this paper is to obtain the solution of fractional order linear dierential equation in RLC Circuit by using a Mittag-Leffler-kummer function. The solution of the fractional linear differential equation of the RLC circuit comes in the form of the Mittag-Leffler function.

There is a scopious rise in the study of financial derivatives over the past two or three decades. Mathematical model proposed by Black and Scholes expounds financial derivatives in a more momentous way. The Black-Scholes model on a single asset is a partial differential equation characterizing the behavior of European options. In this article, we introduce the new Sumudu transform iterative method (NSTIM) as a new technique to obtain the analytical solution of time fractional Black-Scholes model involving European options with two assets. The proposed model is the advanced version of the regular Black-Scholes model. Explicit solution of the problem has been obtained with the help of generalized Mittag-Leffer function. The numerical analysis prove that this method is efficacious in solving various problems of financial theory.