Fractional Giona-Roman Equation on Heterogeneous Fractal Structures in External Force Fields and Its Solutions
Keyword(s):
We introduce a heterogeneous fractional Giona-Roman equation (HFGRE) on heterogeneous fractal structure media describing systems involving external force fields. The HFGRE is shown to obey generalized Einstein relation, and its stationary solution is the Boltzmann distribution. It is proved that the asyrnptotic shape of its solution is a stretched Gaussian and that its solution can be expressed in the form of a function of a dimensionless similarity variable for the case of constant potentials, linear potentials, harmonic potentials, analytic potentials, logarithm potentials and generic potentials.
2003 ◽
Vol 326
(3-4)
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pp. 430-440
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2005 ◽
Vol 24
(1)
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pp. 273-278
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2004 ◽
Vol 20
(3)
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pp. 581-586
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2014 ◽
Vol 156
(6)
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pp. 1111-1124
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1998 ◽
Vol 208
(1)
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pp. 226-240
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1998 ◽
Vol 253
(1-4)
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pp. 205-210
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1973 ◽
Vol 16
(6)
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pp. 675-679
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