JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (10): 89-94.doi: 10.6040/j.issn.1671-9352.0.2014.371
WANG Xue-bin
CLC Number:
| [1] DATSKO B Y, GAFIYCHUK V V. Mathematical modeling of fractional reaction-diffusion systems with different order time derivatives[J]. Journal of Mathematical Sciences, 2010, 165(3):392-402. [2] HILFER R. Applications of fractional calculus in physics[M]. Singapore: World Scientific, 2000. [3] CARPINTERI A, MAINARDI F. Fractals and fractional calculus in continuum mechanics[M]. New York: Springer, 1997: 291-348. [4] METZLER R. Non-homogeneous random walks, generalised master equations, fractional Fokker-Planck equations, and the generalised Kramers-Moyal expansion[J]. The European Physical Journal B: Condensed Matter and Complex Systems, 2001, 19(2):249-258. [5] KEMPPAINEN J. Existence and uniqueness of the solution for a time-fractional diffusion equation[J]. Fractional Calculus and Applied Analysis, 2011, 14(3):411-417. [6] 王学彬.二维、三维空间Riesz分数阶扩散方程的基本解[J].山东大学学报:理学版,2011,46(8):23-30. WANG Xuebin.Fundamental solutions of fractional-in-space diffusion equation with Riesz fractional derivative in two and three dimensions[J]. Journal of Shandong University: Natural Science, 2011, 46(8):23-30. [7] 王学彬,刘发旺.二维和三维的时间分数阶电报方程的解析解[J].山东大学学报:理学版,2012,47(8):114-121. WANG Xuebin, LIU Fawang. Analytical solutions of the time-fractional telegraph equation in two and three dimensions[J]. Journal of Shandong University: Natural Science, 2012, 47(8):114-121. [8] JIANG Hui, LIU Fawang, TURNER I, et al. Analytical solutions for the multi-term time—space Caputo—Riesz fractional advection—diffusion equations on a finite domain[J]. J Math Anal Appl, 2012, 389:1117-1127. [9] PODLUBNY I. Fractional differential equations[M]. New York: Academic Press, 1999. [10] GORENFLO R, MAINARDI F. Random walk models for space-fractional diffusion processes[J]. Fract Calc Appl Anal, 1998, (1):167-191. [11] DIMOVSKI I H. Convolution calculus[M]. Sofia: Bulgarian Academy of Science, 1982. [12] LUCHKO Y, GORENFLO R. An operational method for solving fractional diffenertial equations with the Caputo derivatives[J]. Acta Math Vietnam, 1999, 24(6):207-233. |
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