A new fractional derivative and its application to explanation of polar bear hairs

On two-scale dimension and its applications

“…For 1-D heat conduction through a porous medium, the two-scale dimension can be calculated: eq eq 0 LL LL   (11) where Leq is illustrated in fig. 3 and L is the length of the porous tube.…”

Application of he’s fractional derivative and fractional complex transform for time fractional Camassa-Holm equation

“…The literature has witnessed that the fractal/fractional derivatives have attained much consideration of physicists, mathematicians and engineers in the past three decades because of their realistic behaviors. In the field of engineering and other sciences, different kinds of interdisciplinary problems had been modeled using fractional/fractal derivatives [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] but still it is not easy to find the exact solutions of fractional differential equations. Many analytical and approximation methods [21][22][23][24][25][26][27] have recently been presented to solve linear and non-linear fractional differential equations.…”

A new fractional model for convective straight fins with temperature-dependent thermal conductivity

“…), the plethora of research papers published in scientific journals (e. g. Kumar et al [18] studied differential-difference equation of fractional order, Singh et al [19] investigated the local fractional Tricomi equation, Bhrawy et al [20] examined the fractional Burgers' equations, Area et al [21] analyzed the Ebola epidemic model of fractional order, Carvalho and Pinto [22] presented a delay mathematical model of fractional order to determine the co-infection of malaria and the human immunodeficiency virus, Srivastava et al [23] examined a fractional model of vibration equation, Yang et al [24] studied the fractional KdV equation involving local fractional derivative, Jafari et al [25] investigated the differential equations pertaining to local fractional operators, Yang et al [26] examined the local fractional diffusion and relaxation equations, He at al. [27] studied a new fractional derivative and its application to explanation of polar bear hairs, Wang and Liu [28] showed the applications of He's fractional derivative for non-linear fractional heat transfer equation, Liu et al [29] used the He's fractional derivative for heat conduction in a fractal medium arising in silkworm cocoon hierarchy, Sayevand and Pichaghchi [30] studied a non-linear fractional KdV equation based on He's fractional derivative, Hu et al [31] studied fractal space-time and fractional calculus, Liu et al [32] presented a fractional model for insulation clothings with cocoon-like porous structure, etc.) and definitions of various derivatives and integrals (e. g. Caputo [33], Yang [34], He [35,36], etc.).…”