Exact solutions of the fractional time‐derivative Fokker–Planck equation: A novel approach

2021 ◽  
Author(s):  
Hamdy I. Abdel‐Gawad ◽  
Nasser H. Sweilam ◽  
Seham M. Al‐Mekhlafi ◽  
Dumitru Baleanu
Keyword(s):  
Exact Solutions ◽  
Time Derivative ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Novel Approach ◽  
Fractional Time Derivative ◽  
Fokker Planck

scholarly journals Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 651 ◽  
Author(s):  
Piotr Weber ◽  
Piotr Bełdowski ◽  
Martin Bier ◽  
Adam Gadomski
Keyword(s):  
Entropy Production ◽  
Colloidal Suspension ◽  
Time Derivative ◽  
Planck Equation ◽  
Small Granule ◽  
Fokker Planck Equation ◽  
Self Similar ◽  
Set Up ◽  
Fractional Time Derivative ◽  
Fokker Planck

We study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k B T , which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar in its structure. The subdiffusion that emerges in such a high-dimensional, fractal environment leads to a Fokker–Planck Equation with a fractional time derivative. We set up such a so-called fractional Fokker–Planck Equation for the aggregation into granules. From that Fokker–Planck Equation, we derive an expression for the entropy production of a growing granule.

Exact solutions of the Fokker–Planck equation from an nth order supersymmetric quantum mechanics approach

2009 ◽  
Vol 373 (18-19) ◽  
pp. 1610-1615 ◽  
Author(s):  
Axel Schulze-Halberg ◽  
Jesús Morales Rivas ◽  
José Juan Peña Gil ◽  
Jesús García-Ravelo ◽  
Pinaki Roy
Keyword(s):  
Quantum Mechanics ◽  
Exact Solutions ◽  
Planck Equation ◽  
Supersymmetric Quantum Mechanics ◽  
Fokker Planck Equation ◽  
Fokker Planck
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