“…Most fractional equations are generated by solving specific problems of science and engineering, for example the gas permeability of a nanofiber membrane, [1][2][3][4][5][6] moisture permeability through a cocoon, 7,8 nanoscale multiphase flow, 9 solvent evaporation in the bubble electrospinning, [10][11][12] oscillators arising in microphysics and tsunami motion, 13,14 and sound transmission in hierarchic porous medium that can be exactly modeled by fractional calculus. [15][16][17] There are many fractional derivatives in literature, which are incompatible with each other, among which He's fractional derivative, 15 the local fractional derivative, [18][19][20] the Riemann-Liouville fractional derivative, the Caputo fractional derivative, the Hadamard fractional derivative, and the Atangana-Baleanu fractional derivative 21 are widely used.…”