Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects

Abstract

We herein report a new class of impulsive fractional stochastic differential systems driven by mixed fractional Brownian motions with infinite delay and Hurst parameter H^∈(1/2,1). Using fixed point techniques, a q-resolvent family, and fractional calculus, we discuss the existence of a piecewise continuous mild solution for the proposed system. Moreover, under appropriate conditions, we investigate the approximate controllability of the considered system. Finally, the main results are demonstrated with an illustrative example.

Optimal Defined Contribution Pension Management with Jump Diffusions and Common Shock Dependence

“…where 1 , 2 , 3 and 4 are given by Equation (15), Equation ( 16), Equation (17) and Equation (18), respectively. By Equations ( 13) and ( 14), we have…”

“…Stochastic processes are commonly used to model the uncertainty in the financial market. For further study of stochastic processes, we refer interested readers to [14][15][16][17][18][19][20]. In our paper, we assume that the pension manager is allowed to invest in two types of assets: the bond and the stock.…”

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New Stability Results for Abstract Fractional Differential Equations with Delay and Non-Instantaneous Impulses

“…Mathematical models involving impulsive differential equations and inclusions are used to describe these situations. Several mathematical results, such as the existence of solutions and their asymptotic behavior, have been obtained thus far [33][34][35][36][37] (and references therein).…”