Series Solution Method for Solving Sequential Caputo Fractional Differential Equations

Abstract

Computing the solution of the Caputo fractional differential equation plays an important role in using the order of the fractional derivative as a parameter to enhance the model. In this work, we developed a power series solution method to solve a linear Caputo fractional differential equation of the order q,0<q<1, and this solution matches with the integer solution for q=1. In addition, we also developed a series solution method for a linear sequential Caputo fractional differential equation with constant coefficients of order 2q, which is sequential for order q with Caputo fractional initial conditions. The advantage of our method is that the fractional order q can be used as a parameter to enhance the mathematical model, compared with the integer model. The methods developed here, namely, the series solution method for solving Caputo fractional differential equations of constant coefficients, can be extended to Caputo sequential differential equation with variable coefficients, such as fractional Bessel’s equation with fractional initial conditions.

Research on Human-Robot Collaboration Method for Parallel Robots Oriented to Segment Docking

“…The inherent memory characteristic of fractional-order derivatives can enhance the transient response of the control system, thereby enhancing the closed-loop system’s performance. Mathematically, various definitions of fractional-order derivatives exist [ 24 ]. This paper is mainly concerned with the solution of fractional-order differential equations using the Laplace transform, so the Caputo definition is used in this paper.…”