Fokker-Planck方程的谱非整数导数表示及精确谱导数离散有限差分法
Spectral Non-integer Derivative Representations and the Exact Spectral Derivative Discretization Finite Difference Method for the Fokker-Planck Equation
摘要：
为精确自同原理（SSP）引入了通用差商表示，作为[Clemence-Mkhope，D.P（2021，预印本）中引入的变化率规则。波浪模型的精确谱导数离散有限差分法。arXiv]。属性的基本规则，一个广义导数表示，这是产生一些已知的非整数衍生物的极限情况下，这样的自然衍生措施，这是一些地方的衍生物的整合，分数，或分形类型和非本地衍生物的Caputo和Riemann-Liouville型。提出了一种基于SSP的精确谱导数离散有限差分法，用于求解Fokker-Planck非分数阶和时间分数阶方程，得到的离散模型准确地恢复了一些已知的行为，如Gibbs-Boltzmann分布和Einstein-Stokes-Smoluchowski关系，并预测了新的行为.
英文摘要：
Universal difference quotient representations are introduced for the exact self-sameness principles (SSP) as rules for rates of change introduced in [Clemence-Mkhope, D.P (2021, Preprint). The Exact Spectral Derivative Discretization Finite Difference (ESDDFD) Method for Wave Models. arXiv]. Properties are presented for the fundamental rule, a generalized derivative representation which is shown to yield some known non-integer derivatives as limit cases of such natural derivative measures; this is shown for some local derivatives of conformable, fractional, or fractal type and non-local derivatives of Caputo and Riemann-Liouville type. The SSP-inspired exact spectral derivative discretization finite difference method is presented for the Fokker-Planck non-fractional and time-fractional equations; the resulting discrete models recover exactly some known behaviors predicted for the processes modeled, such as the Gibbs-Boltzmann distribution and the Einstein-Stokes-Smoluchowski relation; new ones are predicted.
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