Browsing by Author "Yadav, Mahaveer Prasad"

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Citation Count: Agarwal, R...et al. (2019). "Analytic Solution of Space Time Fractional Advection Dispersion Equation With Retardation for Contaminant Transport in Porous Media",Progress in Fractional Differentiation and Applications, Vol. 5, No. 4, pp. 283-295.
Analytic Solution of Space Time Fractional Advection Dispersion Equation With Retardation for Contaminant Transport in Porous Media
(Natural Sciences Publishing Corporation, 2019) Agarwal, Ritu; Yadav, Mahaveer Prasad; Agarwal, Ravi; Baleanu, Dumitru; 56389
Motivated by recent applications of fractional calculus, in this paper, we derive analytical solutions of fractional advection-dispersion equation with retardation by replacing the integer order partial derivatives with fractional Riesz-Feller derivative for space variable and Caputo fractional derivative for time variable. The Laplace and Fourier transforms are applied to obtain the solution in terms of the Mittag-Leffler function. Some interesting special cases of the time-space fractional advection-dispersion equation with retardation are also considered. The composition formulas for Green function has been evaluated which enables us to express the solution of the space time fractional advection dispersion equation in terms of the solution of space fractional advection dispersion equation and time fractional advection dispersion equation. Furthermore, from this representation we derive explicit formulae, which enable us to plot the probability densities in space for the different values of the relevant parameters.
Citation Count: Agarwal, Ritu...et al. (2020). "Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative", AIMS Mathematics, Vol. 5, No. 2, pp. 1062-1073.
Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative
(2020) Agarwal, Ritu; Yadav, Mahaveer Prasad; Baleanu, Dumitru; Purohit, S. D.; 56389
In this paper, we discuss the phenomenon of miscible flow with longitudinal dispersion in porous media. This process simultaneously occur because of molecular diffusion and convection. Here, we analyze the governing differential equation involving Caputo-Fabrizio fractional derivative operator having non singular kernel. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. We apply Laplace transform and use technique of iterative method to obtain the solution. Few applications of the main result are discussed by taking different initial conditions to observe the effect on derivatives of different fractional order on the concentration of miscible fluids.