Baleanu, DumitruBaleanu, DumitruWu, Guo-ChengZeng, Sheng-Da2020-03-052020-03-052017Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da, "Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations", Chaos Solitons&Fractals, Vol.102, pp.99-105, (2017).0960-0779https://hdl.handle.net/20.500.12416/2601This paper investigates chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative. A semi-analytical method is proposed based on Adomian polynomials and a fractional Taylor series. Furthermore, chaotic behavior of a fractional Lorenz equation are numerically discussed. Since the fractional derivative includes two fractional parameters, chaos becomes more complicated than the one in Caputo fractional differential equations. Finally, Lyapunov stability is defined for the generalized fractional system. A sufficient condition of asymptotic stability is given and numerical results support the theoretical analysis.eninfo:eu-repo/semantics/closedAccessGeneralized Caputo DerivativeLyapunov Direct MethodAsymptotic StabilityChaosAdomian Decomposition MethodNumerical SolutionsArticle1029910510.1016/j.chaos.2017.02.007