Numerical solution of coupled type Fractional order Burgers' equation using Finite Difference and Fibonacci Collocation Method

In this article a non-standard finite difference collocation method is developed with the help of Fibonacci polynomial to solve the coupled type fractional order Burgers' equation. To show the efficiency of the method, it is used to solve the coupled Burgers' equation having exact solutions and compared the obtained numerical results with the existing results through error analysis. Through the tabular presentation of the results, it is shown that the proposed method is performing much better as compared to the existing methods even for less degree of approximation and less order of temporal discretization. After validation, the method is used for solving an unsolved nonlinear fractional order coupled Burgers' equation and simulate the results for different fractional order spatial derivative for different values of the parameters.