A meshless method for the variable-order time fractional telegraph equation

Abstract

In this paper‎, ‎the radial basis functions (RBFs) method is used for solving a class of variable-order time fractional telegraph equation (V-TFTE)‎, ‎which appears extensively in various fields of science and engineering‎. ‎Fractional derivatives based on Caputo's fractional derivative as a function of the independent variable are defined of order $1<\alpha(x,t)\leq2$‎. ‎The proposed method combines the radial basis functions and finite difference scheme to produce a semi-discrete algorithm‎. ‎In the first stage the variable-order time-dependent derivative is discreticized‎, ‎and then we approximate the solution by the radial basis functions‎. ‎The aim of this paper is to show that the collocation method based on RBFs is suitable for the treatment of the variable-order fractional partial differential equations‎. ‎The efficiency and accuracy of the proposed method are shown for some concrete examples‎. ‎The results reveal that the proposed method is very efficient and accurate‎.