“…On the contrary, fractional-order derivative has nonlocal characteristics; based on this property, the fractional differential equation can also interpret many abnormal phenomena that occur in applied science and engineering, such as viscoelastic dynamical phenomena [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], advection-dispersion process in anomalous diffusion [30][31][32][33][34], and bioprocesses with genetic attribute [35,36]. As a powerful tool of modeling the above phenomena, in recent years, the fractional calculus theory has been perfected gradually by many researchers, and various different types of fractional derivatives were studied, such as Riemann-Liouville derivatives [16,, Hadamardtype derivatives [63][64][65][66][67][68][69][70][71], Katugampola-Caputo derivatives [72], conformable derivatives [73][74][75][76], Caputo-Fabrizio derivatives [77,78], Hilfer derivatives …”