Abstract
In this paper, we obtain an approximate/analytical solution of nonlinear fractional diffusion equation using the q-homotopy analysis transform method. The existence and uniqueness of the solution for this problem are also derived. Further, the applicability of the model is discussed based on graphical results and numerical examples.
Highlights
Many phenomena of the physical sciences are associated with the idea of diffusion like populations of different kinds diffuse; particles in a solvent and other substances diffusing; ions diffusing and electrons; and the momentum of a viscous fluid diffusing
The type of partial differential equations (PDEs) used is the so-called parabolic equations, a family based on the properties of the most classical model, the linear heat equation, which is called in this context the diffusion equation
Nonlinear diffusion equations are a generalization of diffusion and it comes from a variety of diffusion phenomena which appear widely in nature
Summary
Many phenomena of the physical sciences are associated with the idea of diffusion like populations of different kinds diffuse; particles in a solvent and other substances diffusing; ions diffusing and electrons; and the momentum of a viscous fluid diffusing. The detailed derivation of the nonlinear diffusion equation can be found in [2]. We consider the Laplace transform for the fractional differential operator for n = 1. Definition 2.2 ([24]) Consider g is a function continuous on [a, b], the Laplace transform for AB-derivative is defined as
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