Exact Solutions and Their Asymptotic Behaviors for the Averaged Generalized Fractional Elastic Models |
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| Authors: | LI Can DENG Wei-Hua SHEN Xiao-Qin |
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| Affiliation: | 1. Department of Applied Mathematics, School of Sciences, Xi'an University of Technology, Xi'an 710054, China;2. School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, China;3. Kavli Institute for Theoretical Physics China, CAS, Beijing 100190, China |
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| Abstract: | The generalized fractional elastic models govern the stochastic motion of several many-body systems, e.g., polymers, membranes, and growing interfaces. This paper focuses on the exact formulations and their asymptotic behaviors of the average of the solutions of the generalized fractional elastic models. So we directly analyze the Cauchy problem of the averaged generalized elastic model involving time fractional derivative and the convolution integral of a radially symmetric friction kernel with space fractional Laplacian. |
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| Keywords: | Fourier transform Laplace transform Fox's H-function Green's functions asymptotic behaviors |
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