Fractional Itô–Doob Stochastic Differential Equations Driven by Countably Many Brownian Motions-Reference-Cited by-同舟云学术

Fractional Itô–Doob Stochastic Differential Equations Driven by Countably Many Brownian Motions

Published:2023-04-16 Issue:4 Volume:7 Page:331
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Ben Makhlouf Abdellatif¹^ORCID,Mchiri Lassaad²,Othman Hakeem A.³^ORCID,Rguigui Hafedh M. S.³

Affiliation:

1. Department of Mathematics, College of Science, Jouf University, Sakaka 72388, Saudi Arabia

2. ENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes, CEDEX, France

3. Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al-Qunfudhah 24382, Saudi Arabia

Abstract

This article is devoted to showing the existence and uniqueness (EU) of a solution with non-Lipschitz coefficients (NLC) of fractional Itô-Doob stochastic differential equations driven by countably many Brownian motions (FIDSDECBMs) of order ϰ∈(0,1) by using the Picard iteration technique (PIT) and the semimartingale local time (SLT).

Funder

The Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/4/331/pdf

Reference16 articles.

1. Riemann–Liouville and Caputo Fractional Potentials Associated with the Number Operator;Alhussain;Complex Anal. Oper. Theory,2022

2. Atanackovic, T.M., Pilipovic, S., Stankovic, B., and Zorica, D. (2014). Fractional Calculus with Applications in Mechanics, Wiley-ISTE.

3. Baleanu, D., Machado, J.A., and Luo, A.C. (2011). Fractional Dynamics and Control, Springer Science and Business Media.

4. Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier.

5. Ulam–Hyers stability of pantograph fractional stochastic differential equations;Mchiri;Math. Methods Appl. Sci.,2023