论文标题
Volterra-Prabhakar的分布式订单和某些应用
Volterra-Prabhakar derivative of distributed order and some applications
论文作者
论文摘要
本文研究了两种广义的fokker-planck方程的精确解决方案，其中积分内核由分布式订单函数$ k_ {1}（t）= \ int_ {0}^{1}^{1} t^{1} t^{ - μ}/γ（1-μ）dμ$ $或分布式prabhakar prabhakar function; t）= \ int_ {0}^{1} e^{ - γ} _ {α，1-μ}（λ; t）dμ$，其中prabhakar函数表示为$ e^{ - γ} _ { - γ} _ {α，α，1-μ}（λ}（λ;λ;λ; t）$。这两个积分内核都可以称为褪色内存函数，并且是stieltjes函数。还表明他们的stieltjes特征足以确保均方根值和更高的矩。奇怪的时刻消失了。因此，可以称为概率密度函数的广义fokker-planck方程的解决方案。我们还介绍了Volterra-prabhakar函数及其概括，这些功能涉及$ k_ {2}（α，γ;λ; t）$的定义，并由其生成的概率密度函数$ p_2（x，t）$。
The paper studies the exact solution of two kinds of generalized Fokker-Planck equations in which the integral kernels are given either by the distributed order function $k_{1}(t) = \int_{0}^{1} t^{-μ}/Γ(1- μ) dμ$ or the distributed order Prabhakar function $k_{2}(α, γ; λ; t) = \int_{0}^{1} e^{-γ}_{α, 1 - μ}(λ; t) dμ$, where the Prabhakar function is denoted as $e^{-γ}_{α, 1 - μ}(λ; t)$. Both of these integral kernels can be called the fading memory functions and are the Stieltjes functions. It is also shown that their Stieltjes character is enough to ensure the non-negativity of the mean square values and higher even moments. The odd moments vanish. Thus, the solution of generalized Fokker-Planck equations can be called the probability density functions. We introduce also the Volterra-Prabhakar function and its generalization which are involved in the definition of $k_{2}(α, γ; λ; t)$ and generated by it the probability density function $p_2(x, t)$.
