Exact solutions for nonlinear fractional anomalous diffusion equations |
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Authors: | Jin-Rong Liang Fu-Yao Ren |
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Affiliation: | a Department of Mathematics, East China Normal University, Shanghai 200062, China b Department of Mathematics, Fudan University, Shanghai 200433, China c School of Science, Hangzhou Dianzi University, Hangzhou 310037, China |
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Abstract: | This work is devoted to investigating exact solutions of generalized nonlinear fractional diffusion equations with external force and absorption. We first investigate the nonlinear anomalous diffusion equations with one-fractional derivative and then multi-fractional ones. In both situations, we obtain the corresponding exact solution, its diffusive behavior, and the sufficient and necessary conditions for solutions satisfying the boundary condition W(±∞,t)=0 and the sharp initial condition W(x,0)=δ(x). |
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Keywords: | Anomalous diffusion Fractional derivative Fractional diffusion equation |
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