Meshfree numerical integration for some challenging multi-term fractional order PDEs

Abstract

<abstract><p>Fractional partial differential equations (PDEs) have key role in many physical, chemical, biological and economic problems. Different numerical techniques have been adopted to deal the multi-term FPDEs. In this article, the meshfree numerical scheme, Radial basis function (RBF) is discussed for some time-space fractional PDEs. The meshfree RBF method base on the Gaussian function and is used to test the numerical results of the time-space fractional PDE problems. Riesz fractional derivative and Grünwald-Letnikov fractional derivative techniques are used to deal the space fractional derivative terms while the time-fractional derivatives are iterated by Caputo derivative method. The accuracy of the suggested scheme is analyzed by using $ L_\infty $-norm. Stability and convergence analysis are also discussed.</p></abstract>