In this work, the theoretical study of steady flow for lift and drainage of Power law MHD fluid on a vertical cylinder is presented. The governing nonlinear differential equation has been derived from the momentum equation. The resulting equation is then solved using Perturbation method. Series solutions have been obtained for velocity, flow rate and average velocity in both cases. The graphica...

This study has been motivated by the observed difference in the range of the power-law attenuation exponent for compressional and shear waves. Usually compressional attenuation increases with frequency to a power between 1 and 2, while shear wave attenuation often is described with powers less than 1. Another motivation is the apparent lack of partial differential equations with desirable prope...

Fractional partial differential equations with more than one fractional derivative term in time, such as the Szabo wave equation, or the power law wave equation, describe important physical phenomena. However, studies of these multi-term time-space or time fractional wave equations are still under development. In this paper, multi-term modified power law wave equations in a finite domain are co...

We analyze the generalized time-dependent Schrödinger equation for the force free case, as a generalization, for example, of the standard time-dependent Schrödinger equation, time fractional Schrödinger equation, distributed order time fractional Schrödinger equation, and tempered in time Schrödinger equation. We relate it to the corresponding standard Schrödinger equation with effective potent...

In this study, predictive capabilities of apparent viscosity of oil-based drilling fluids which is used in National Iranian South Oilfields Company (NISOC) were evaluated using Newtonian and non-Newtonian models to drive a new suitable equation. The non-Newtonian models include Bingham plastic, Power law, Herschel-Bulkley, Casson, and Robertson-Stiff. To validate the results, the calculated vis...

From the available literature, the allometric scaling laws generally exist in biology, ecology, etc. These scaling laws obey power law distributions. A possibly better approach to characterize the power law is to utilize fractional derivatives. In this paper, we establish a fractional differential equation model for this allometry by using the Caputo fractional derivatives.

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foe...