Rashid Ashraf

Abdul Wali Khan University Mardan · Mathematics

In this article, approximate solutions of some PDE of fractional order are investi­gated with the help of a new semi-analytical method called the optimal auxiliary function method. The proposed method was tested upon the time-fractional Fisher equation, the time-fractional Fornberg-Whitham equation, and the time-fractional Inviscid Burger equation....

This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann–Liouville’s fractional integral and the Caputo derivative. This approach eliminates the need for assumptions about parameter magnitudes, offering a significant advantage. We validate our ap...

In this article, a semi-analytical approach known as the optimal auxiliary function method is extended to the approximate solution of non-linear partial differential equations. The fifth-order lax and swada-kotera equations are taken as test examples. Utilizing the well-known least squares method, the optimal convergence control parameter values in...