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.
- Design Engineering Division and Computers and Information in Engineering Division
Fractional Giona-Roman Equation on Heterogeneous Fractal Structures in External Force Fields and Its Solutions
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Ren, F, Liang, J, Qiu, W, & Xu, Y. "Fractional Giona-Roman Equation on Heterogeneous Fractal Structures in External Force Fields and Its Solutions." Proceedings of the ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C. Chicago, Illinois, USA. September 2–6, 2003. pp. 843-848. ASME. https://doi.org/10.1115/DETC2003/VIB-48401
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