2023/04/20 by Guo-Cheng Wu, Guo–Cheng Wu, Jia-Li Wei +1
Mathematics · Physics and Astronomy · #Chaos control and synchronization #Fractional Differential Equations Solutions #Mathematical Dynamics and Fractals
paper · doi:10.1080/10236198.2023.2198043
openalex publication_date 2023/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06
Inverse or terminal value problems of fractional differential equations become popular recently. But memory effects or non-locality of fractional operators cause many difficulties for theoretical analysis. This study suggests a right fractional calculus method for inverse problem modelling and proposes a concept of inverse-time fractional chaotic maps. First, a simple right fractional linear differential equation's terminal value problem and the solutions are investigated. Then, some basics of the right discrete fractional calculus are introduced and the idea is extended to the discrete case. Right fractional sum equations are derived and numerical schemes are provided for dynamical analysis. Discrete chaos does exist in an inverse-time fractional logistic map and Hénon map, respectively. Their local stability conditions are given. It can be concluded that this right fractional calculus method is simpler but more efficient than the left one.