Fractional differential quadrature techniques for fractional order Cauchy reaction‐diffusion equations

Abstract

This paper aims to explore and apply differential quadrature based on different test functions to find an efficient numerical solution of fractional order Cauchy reaction‐diffusion equations (CRDEs). The governing system is discretized through time and space via novel techniques of differential quadrature method and the fractional operator of Caputo kind. Two problems are offered to explain the accuracy of the numerical algorithms. To verify the reliability, accuracy, efficiency, and speed of these methods, computed results are compared numerically and graphically with the exact and semi‐exact solutions. Then mainly, we deal with absolute errors and L∞ errors to study the convergence of the presented methods. For each technique, MATLAB Code is designed to solve these problems with the error reaching ≤1 × 10−5. In addition, a parametric analysis is presented to discuss influence of fractional order derivative on results. The achieved solutions prove the viability of the presented methods and demonstrate that these methods are easy to implement, effective, high accurate, and appropriate for studying fractional partial differential equations emerging in fields related to science and engineering.