Applications of Separation Variables Approach in Solving Time-Fractional PDEs

A Novel Effective Approach for Solving Fractional Nonlinear PDEs

The present work introduces an effective modification of homotopy perturbation method for the solution of nonlinear time-fractional biological population model and a system of three nonlinear time-fractional partial differential equations. In this approach, the solution is considered a series expansion that converges to the nonlinear problem. The new approximate analytical procedure depends onl...

Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations

A new method proposed and coined by the authors as the homo-separation of variables method is utilized to solve systems of linear and nonlinear fractional partial differential equations (FPDEs). The new method is a combination of two well-established mathematical methods, namely, the homotopy perturbation method (HPM) and the separation of variables method. When compared to existing analytical ...

Wavelets: An Alternative Approach to Solving PDEs

Parallelism in Solving PDEs

This paper examines the potential of parallel computation methods for partial differential equations (PDEs). We first observe that linear algebra does not give the best data structures for exploiting parallelism in solving PDEs, the data structures should be based on the physical geometry. There is a naturally high level of parallelism in the physical world to be exploited and we show there is ...