Numerical Solution of Distributed-Order Time Fractional Klein-Gordon System

Abstract

In this work, the distributed-order time fractional Klein-Gordon-Zakharov system is introduced by substituting the second-order temporal derivative with a distributed-order fractional derivative. The Caputo fractional derivative is utilized to define this kind of distributed-order fractional derivative. A high accuracy approach based on the Chebyshev cardinal polynomials is established for this system. The proposed method turns the fractional system solution into an algebraic system solution by approximating the unknown solution via these cardinal polynomials and engaging their derivative matrices (that are obtained in this paper). Some test problems are considered to investigate the capability and accuracy of this approach.