Differential Electromagnetic Equations in Fractional Space

Author(s):  
Muhammad Zubair ◽  
Muhammad Junaid Mughal ◽  
Qaisar Abbas Naqvi
Keyword(s):  
2020 ◽  
Vol 11 (1) ◽  
pp. 1-12 ◽  
Author(s):  
M. Levent Kavvas ◽  
Tongbi Tu ◽  
Ali Ercan ◽  
James Polsinelli

Abstract. In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.


Open Physics ◽  
2007 ◽  
Vol 5 (3) ◽  
Author(s):  
Sami Muslih ◽  
Dumitru Baleanu ◽  
Eqab Rabei

AbstractIn this paper the gravitational potential with β-th order fractional mass distribution was obtained in α dimensionally fractional space. We show that the fractional gravitational universal constant G α is given by $$G_\alpha = \frac{{2\Gamma \left( {\frac{\alpha }{2}} \right)}}{{\pi ^{\alpha /2 - 1} (\alpha - 2)}}G$$ , where G is the usual gravitational universal constant and the dimensionality of the space is α > 2.


2007 ◽  
Vol 13 (9-10) ◽  
pp. 1209-1216 ◽  
Author(s):  
Sami I. Muslih ◽  
Dumitru Baleanu

Fractals ◽  
2021 ◽  
Author(s):  
WAEL W. MOHAMMED ◽  
NAVEED IQBAL

In this paper, we present a class of stochastic system of fractional space diffusion equations forced by additive noise. Our goal here is to approximate the solutions of this system via a system of ordinary differential equations. Moreover, we study the influence of the same degenerate additive noise on the stability of the solutions of the stochastic system of fractional diffusion equations. We are interested in the systems that have nonlinear polynomial and give applications as Lotka–Volterra system from biology and the Brusselator model for the Belousov–Zhabotinsky chemical reaction from chemistry to illustrate our results.


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