Closure: to “Discussion on the Paper ‘Synchronization Via Fractal–Fractional Differential Operators on Two-Mass Torsional Vibration System Consisting of Motor and Roller,’ Abro, K. A., and Atangana, A., 2021, ASME J. Comput. Nonlinear Dyn., 16(12), p. 12

Abstract

The authors are thankful to Professor Asterios Pantokratoras, School of Engineering, Democritus University, for his comments on our paper. His comments prompted us to double-check our paper. After double checking all equations, we found that indeed the parameters of equations were dimensionally homogenous. It is confirmed that the parameters of equations were dimensionally homogenous as defined in Ref. [1].The specific parameter values have been described by the authors in the paper with dimensionless quantities/parameters. For the sake of clarity, the values parameters used in numerical simulations as: b1=2.03, b3=0.88, c2=1.73, c3=0.11, d1=3.47,d2=3.86, l1=0.96,l2=1.16, l3=1.29, m=0.056, n=−0.6, σ1=σ3=σ5=0.98,σ2=σ4=σ6=0.99. In our published paper [2], novel differential operators called fractal-fractional derivatives were applied. We have followed Ref. [1] and utilized the novel application of fractal-fractional differential and integral operators.