Volterra-Prabhakar function of distributed order and some applications

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Volterra-Prabhakar function of distributed order and some applications

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

Volterra-Prabhakar function of distributed order and some applications

Popis výsledku anglicky

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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

J COMPUT APPL MATH

ISSN

0377-0427

e-ISSN

1879-1778

Svazek periodika

—

Číslo periodika v rámci svazku

433

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

21

Strana od-do

1-21

Kód UT WoS článku

001002012400001

EID výsledku v databázi Scopus

2-s2.0-85159305149