Volterra-Prabhakar function of distributed order and some applications
Identifikátory výsledku
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>
Alternativní jazyky
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).
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10102 - Applied mathematics
Návaznosti výsledku
Projekt
—
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
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