Analysis of Generalized Nonlinear Quadrature for Novel Fractional-Order Chaotic Systems Using Sinc Shape Function

Abstract

This paper introduces the generalized fractional differential quadrature method, which is based on the generalized Caputo type and is used for the first time to solve nonlinear fractional differential equations. One of the effective shape functions of this method is the Cardinal Sine shape function, which is used in combination with the fractional operator of the generalized Caputo kind to convert nonlinear fractional differential equations into a nonlinear algebraic system. The nonlinearity problem is then solved using an iterative approach. Numerical results for a variety of chaotic systems are introduced using the MATLAB program and compared with previous theoretical and numerical results to ensure their reliability, convergence, accuracy, and efficiency. The fractional parameters play an effective role in studying the proposed problems. The achieved solutions prove the viability of the presented method and demonstrate that this method is easy to implement, effective, highly accurate, and appropriate for studying fractional differential equations emerging in fields related to chaotic systems and generalized Caputo-type fractional problems in the future.