Volterra-Prabhakar function of distributed order and some applications

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F23%3AA2402L46" target="_blank" >RIV/61988987:17310/23:A2402L46 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0377042723002509" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0377042723002509</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cam.2023.115306" target="_blank" >10.1016/j.cam.2023.115306</a>

Result language
angličtina
Original language name
Volterra-Prabhakar function of distributed order and some applications
Original language description
The paper studies the exact solution of two kinds of generalized Fokker-Planck equa-tions in which the integral kernels are given either by the distributed order function k_1(t) = integral 0^1 t-mu/Gamma(1 - mu)dmu or the distributed order Prabhakar function k_2(alpha, gamma; lambda; t) = integral 0^1 e-gamma alpha,1-mu(lambda; t) dmu, where the Prabhakar function is denoted as e-gamma alpha,1-mu(lambda; 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(alpha, gamma; lambda; t) and generated by it the probability density function p_2(x, t).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)