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 Â 10 À5 . 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.

Extended Laplace Power Series Method for Solving Nonlinear Caputo Fractional Volterra Integro-Differential Equations

“…For instance, robotics, nonlinear oscillations of earthquakes, control theory, signal processing, and viscoelasticity [4][5][6][7]. For more details and applications of FC, we refer the reader to [8][9][10][11][12][13][14]. Since the ordinary differential is a local operator, but the fractional order differential operator is nonlocal, the nonlocal property is considered the most significant aspect of using fractional differential equations (FDEs), which indicates the following state of a phenomenon does not rely only upon its current state but considers its historical states as well.…”