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Fractional Integral Representation of Master Equation

✍ Scribed by S.A. Elwakil; M.A. Zahran

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
215 KB
Volume
10
Category
Article
ISSN
0960-0779

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✦ Synopsis

Using the de_nition of LiouvilleÐRiemann "LÐR# fractional integral operator\ master equation can be represented in the domain of fractal time evolution with a critical exponent a"9³a¾0#[ The relation between the continuous time random walks "CTRW# and fractional master equation "FME# has been achieved by obtaining the corresponding waiting time density "WTD# c"t#[ The latter is obtained in a closed form in terms of the generalized MittagÐLe/er "MÐL# function[ The asymptotic expansion of the "MÐL# function show the same behavior considered in the theory of random walk[ Applying the Fourier and LaplaceÐMellin transforms to "FME#\ one obtains the solution\ in closed form\ in terms of the Fox function[

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