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This comment is to point out some mistakes made in the paper (Shiva et al in MATH METHOD APPL SCI 42(7):2302‐2323, 2019). The stability of Prabhakar fractional dynamical systems without and with time delay is addressed. Lyapunov stability theorem is extended to these systems. But the proof process is wrong as the memory property of fractional calculus. It is necessary to point out these errors to avoid misleading. Finally, a counterexample is proposed against the proposed theorem. [ABSTRACT FROM AUTHOR]

The paper presents theoretical results on the global asymptotic stability and synchronization of a class of fractional-order memristor-based neural networks (FMNN) with multiple delays. First, the asymptotic stability of fractional-order (FO) linear systems with single or multiple delays is discussed. Delay-independent stability criteria for the two types of systems are established by using the maximum modulus principle and the spectral radii of matrices. Second, new testable algebraic criteria for ensuring the existence and global asymptotic stability of the system equilibrium point are obtained by employing the Kakutani’s fixed point theorem of set-valued maps, the comparison theorem, and the stability criterion for FO linear systems with multiple delays. Third, the synchronization criterion for FMNN is presented based on the linear error feedback control. Finally, numerical examples are given demonstrating the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]