AIMS Mathematics, 2020, 5(2): 843-855. doi: 10.3934/math2020057

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A new approach to solve Cattaneo-Hristov diffusion model and fractional diffusion equations with Hilfer-Prabhakar derivative

1 Amity Institute of information Technology, Amity University, Rajasthan, Jaipur-303002, India
2 Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India
3 Department of Mathematics, Amity University, Rajasthan, Jaipur-303002, India
4 Department of Mathematics, Govt. P. G. College, Hisar, Haryana-125001, India

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In the present article, we investigate complete Cattaneo-Hristov diffusion (CCHD) equation and fractional diffusion equation in one and two dimensional spaces and find their analytic solution by using Elzaki transform technique under the Dirichlet boundary conditions. The fractional diffusion equation describe by the Hilfer-Prabhakar derivative and established the solution in one and two dimensional spaces by using Elzaki and Fourier Sine transform in terms of Mittag-Leffler function. In this paper, we also establish new results such as Elzaki transform of Caputo-Fabrizio and Hilfer-Prabhakar derivative which will be very helpful to find the analytical solution fractional differential equations.
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