Numerical solution of fractional partial differential equations by using radial basis functions combined with Legendre wavelets

This paper presents an approximate method to solve a class of fractional partial differential equations (FPDEs). First, we introduce   radial basis functions (RBFs) combined with wavelets.  Next, we obtain fractional integral operator (FIO) of wavelets-radial basis functions (W-RBFs) directly.  In the next step, the W-RBFs and their FIO  are used to transform the problem under consideration into a  system of algebraic equations, which can be simply solved to achieve the solution of the problem.   Finally, some numerical examples are presented to illustrate the efficiency and accuracy of the method.