# Numerical solution of space-fractional partial differential equations by a differential quadrature approach

## TL;DR

This paper introduces a new differential quadrature method using radial basis functions to efficiently and accurately solve space-fractional PDEs, demonstrating robustness and high precision through numerical tests.

## Contribution

It develops a novel RBF-based differential quadrature technique for space-fractional PDEs, enhancing accuracy and simplicity over existing methods.

## Key findings

- Method is robust and straightforward to implement.
- Achieves high accuracy with proper RBF shape parameters.
- Numerical tests confirm effectiveness and validity.

## Abstract

This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted linear combinations of the function values at discrete grid points on problem domain with the weights calculated via using three types of radial basis functions (RBFs) as test functions. The method in presence is robust, straight forward to apply, and highly accurate under the condition that the shape parameters of RBFs are well chosen. Numerical tests are provided to illustrate its validity and capability.