The meshless Kansa method for time-fractional higher order partial differential equations with constant and variable coefficients

Abstract

In this work, a meshfree technique based on radial basis functions (RBFs) is proposed for the study of time-fractional higher order partial differential equations (PDEs) of constant and variable coefficients. The RBFs used containing shape parameter, the selection of which is not an easy task and affects stability and accuracy of the results. The required shape parameter has been computed with the help of recently developed algorithm in literature. Computer simulations are performed for six different time-fractional PDEs which features excellent agreement with the exact solutions and earlier works. Approximation quality of the computed solutions are assessed via $$E_{2}$$ , $$E_{\infty }$$ and $$E_{\text {rms}}$$ error norms.