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Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials

Wu Guo-Cheng (Neijiang Normal University, College of Mathematics and Information Science, Neijiang, China)
Baleanu Dumitru (Cankaya University, Department of Mathematics and Computer Sciences, Balgat, Ankara, Turkey + Institute of Space Sciences, Magurele, Bucharest, Romania)
Luo Wei-Hua (Neijiang Normal University, College of Mathematics and Information Science, Neijiang, China)

A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.

Keywords: fractional calculus, two fractional terms, numerical solutions, Adomian decomposition method, Taylor series of fractional order