The Wright functions as solutions of the time-fractional diffusion equation
نویسندگان
چکیده
We revisit the Cauchy problem for the time-fractional diffusion equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order b 2 ð0; 2 . By using the Fourier–Laplace transforms the fundamentals solutions (Green functions) are shown to be high transcendental functions of the Wright-type that can be interpreted as spatial probability density functions evolving in time with similarity properties. We provide a general representation of these functions in terms of Mellin–Barnes integrals useful for numerical computation. 2002 Elsevier Science Inc. All rights reserved.
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ورودعنوان ژورنال:
- Applied Mathematics and Computation
دوره 141 شماره
صفحات -
تاریخ انتشار 2003