Deng, WH (reprint author), Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & complex Syst, Lanzhou 730000, Peoples R China.
; Shen Xiao-Qin] Xian Univ Technol, Sch Sci, Dept Appl Math, Xian 710054, Peoples R China
; [Deng Wei-Hua] Lanzhou Univ, Sch Math & Stat, Gansu Key Lab Appl Math & complex Syst, Lanzhou 730000, Peoples R China
; [Deng Wei-Hua] Chinese Acad Sci, Kavli Inst Theoret Phys China, Beijing 100190, Peoples R China
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.