Numerical solution for space and time fractional order Burger type equation

Abstract

In this paper, we study the fractional differential operators thereby considering the space and time order Burger type equation with initial condition. The extended finite difference method which is based on shifted Grünwald, Caputo and Riemann formulas are used. The fractional terms are approximated using two fractional difference schemes. Time Order Burger type Equation, Space Order Burger type Equation and Space-Time Order Burger type Equation are discussed with an example and error estimates obtained for the Finite difference method (FDM) and Generalized Taylor Series Methods (GTSM). The numerical methods have been applied to solve a numerical example, and results are compared with the exact solutions. By these methods, the numerical solutions of space and time order Burger type equation are obtained with the help of Wolfram Mathematica 11 software package. We present the tables of the obtained numerical results. Keywords: Finite difference method, Generalized Taylor series method, Space and time order Burger type equation, Grünwald formula, Caputo formula