Theoretical analysis of time fractal fractional pantograph stochastic differential equations

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10258513" target="_blank" >RIV/61989100:27740/25:10258513 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S2666818125001858?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S2666818125001858?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.padiff.2025.101258" target="_blank" >10.1016/j.padiff.2025.101258</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Theoretical analysis of time fractal fractional pantograph stochastic differential equations

Popis výsledku v původním jazyce

The fractal-fractional derivative, a significant mathematical concept that merges fractal geometry with fractional calculus, has garnered increasing attention for modeling complex systems. To the best of our knowledge, no existing work has addressed the well-posedness, regularity, and averaging principle for fractal-fractional pantograph stochastic differential equations (FFrPSDEs). In this study, we fill this gap by presenting results under the Atangana fractal-fractional derivative with the Riemann–Liouville (RL) definition and a power-law kernel. These equations capture essential features such as fractal behavior, memory effects, nonlocal dynamics, stochasticity, and time delays. We first establish the existence and uniqueness of solutions using a fixed-point approach. Next, we present results on continuous dependence and solution regularity. We also prove an averaging principle that simplifies the analysis of complex systems. Finally, illustrative examples are provided to demonstrate the applicability of the theoretical findings.

Název v anglickém jazyce

Theoretical analysis of time fractal fractional pantograph stochastic differential equations

Popis výsledku anglicky

The fractal-fractional derivative, a significant mathematical concept that merges fractal geometry with fractional calculus, has garnered increasing attention for modeling complex systems. To the best of our knowledge, no existing work has addressed the well-posedness, regularity, and averaging principle for fractal-fractional pantograph stochastic differential equations (FFrPSDEs). In this study, we fill this gap by presenting results under the Atangana fractal-fractional derivative with the Riemann–Liouville (RL) definition and a power-law kernel. These equations capture essential features such as fractal behavior, memory effects, nonlocal dynamics, stochasticity, and time delays. We first establish the existence and uniqueness of solutions using a fixed-point approach. Next, we present results on continuous dependence and solution regularity. We also prove an averaging principle that simplifies the analysis of complex systems. Finally, illustrative examples are provided to demonstrate the applicability of the theoretical findings.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10100 - Mathematics

Projekt

<a href="/cs/project/EH23_021%2F0008759" target="_blank" >EH23_021/0008759: Zvýšení odolnosti energetických sítí v kontextu dekarbonizace, decentralizace a udržitelného socioekonomického rozvoje</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Partial Differential Equations in Applied Mathematics

ISSN

2666-8181

e-ISSN

2666-8181

Svazek periodika

15

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

19

Strana od-do

101258

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-105012992720