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 equa- tion (V-TFTE), which appears extensively in various fields of science tion (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 or- der 1 < α(x, t)  2. The proposed method combines the radial basis functions and finite difference scheme to produce a semi-discrete algo- rithm. 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 frac- tional 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.