In this study, the Homotopy Analysis Transform Method (HATM) is presented to find the analytical solution of a General Fractional Diffusion Equation (GFDE) arising in nano-hydrodynamics. The GFDE is obtained from the standard diffusion equations by replacing the second-order space derivative and first-order time derivative with the space fractional and time fractional derivatives, respectively. Some examples are given to illustrate the high accuracy and efficiency of the proposed method. In addition, the numerical results show that the HATM is easy to implement and accurate for solving GFDE.
Thermally activated flux motion and specific electric resistance in Y358 were studied under different magnetic fields ranging from 0 to 15 kOe. Through investigating the broadening of normal-superconducting transition, we found that the thermally-activated-flux-motion model can describe the electronic effect near the superconducting transition temperature. By modifying this model, specific electric resistance at different magnetic fields was calculated.
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