Formulation of space-angular fractional radiative transfer equation in participating finite slab clumpy media

Space-angular fractional radiative transfer equation has been derived depending on the invariance of the functional potential and the Euler-Lagrange functional of the radiative-transfer intensity. Pomraning-Eddington technique is employed to unzip the space-fractional radiative transfer through a clumpy medium. The medium is considered as an anisotropic scattering participating finite slab with specular reflecting boundaries. The fractional differential operator is taken in terms of the Jumarie Riemann-Liouville representation. The resultant space-fractional equation has diffusion parameter depends on both the single scattering albedo and the anisotropic parameter of the medium. Laplace transformation method is used to solve the obtained space-fractional differential equation, whose solution is obtained in terms of the Mittag-Leffler function. Numerical calculations are carried out to investigate the effects of the fractional exponent and the other radiative-transfer parameters on the radiation density and net flux through the medium. In addition, the reflectivity and transmissivity from the medium boundaries are calculated and represented graphically.