AIMS Mathematics, 2020, 5(2): 1062-1073. doi: 10.3934/math.2020074.

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Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative

1 Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017, India
2 Department of Mathematics, Cankaya University, Ankara-06430, Turkey
3 Institute of Space Sciences, Magurele-Bucharest-R 76900, Romania
4 Department of HEAS(Mathematics), Rajasthan Technical University, Kota-324010, India

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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.
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Citation: Ritu Agarwal, Mahaveer Prasad Yadav, Dumitru Baleanu, S. D. Purohit. Existence and uniqueness of miscible flow equation through porous media with a non singular fractional derivative. AIMS Mathematics, 2020, 5(2): 1062-1073. doi: 10.3934/math.2020074

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