Hadamard Itô-Doob Stochastic Fractional Order Systems
Abdellatif Ben Makhlouf, Lassaad Mchiri, Hassen Arfaoui, Slim Dhahri, El‐sayed El‐hady, Bahri Cherif
Abstract
In this paper, we study the existence and uniqueness of Hadamard Itô-Doob Stochastic Fractional Order Systems (HIDSFOS) using the Picard iteration method. Different from the previous works, our paper presents a new theory using the Hadamard fractional integral. We have proved the convergence of the solution of the averaged HIDSFOS to that of the standard HIDSFOS in the sense of the mean square and also in probability. Some examples are given at the end of this paper to illustrate our theoretical results.
Topics & Concepts
Hadamard transformMathematicsUniquenessApplied mathematicsConvergence (economics)Order (exchange)Mathematical analysisEconomicsFinanceEconomic growthAdvanced Control Systems DesignFractional Differential Equations SolutionsNumerical methods for differential equations