Proportional Itô–Doob Stochastic Fractional Order Systems

Abdellatif Ben Makhlouf (), Lassaad Mchiri, Hakeem A. Othman, Hafedh M. S. Rguigui and Salah Boulaaras
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Abdellatif Ben Makhlouf: Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia
Lassaad Mchiri: ENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes, CEDEX, France
Hakeem A. Othman: Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 28821, Saudi Arabia
Hafedh M. S. Rguigui: Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 28821, Saudi Arabia
Salah Boulaaras: Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Almelida 51452, Saudi Arabia

Mathematics, 2023, vol. 11, issue 9, 1-14

Abstract: In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results.

Keywords: stochastic system; proportional fractional integral (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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