Existence results for random fractional differential equations

Abstract

Abstract. In this paper, an existence result for a random fractional differential equation is established under a Carathéodory condition. Existence results for extremal random solutions are also proved. Finally, an existence and uniqueness result is given.

Fractional Partial Random Differential Equations with State-Dependent Delay

“…We refer the reader to the monographs [18,31,43]. The initial value problems for fractional differential with random parameters have been studied by Lupulescu and Ntouyas [33]. The basic tool in the study of the problems for random fractional differential equations is to treat it as a fractional differential equation in some appropriate Banach space.…”

“…The basic tool in the study of the problems for random fractional differential equations is to treat it as a fractional differential equation in some appropriate Banach space. In [34], the authors proved the existence results for a random fractional equation under a Carathéodory condition.…”

On fractional random differential equations with delay

“…The basic tool in the study of the problems for random fractional differential equations is to treat it as a fractional differential equation in some appropriate Banach space. In [25], authors proved the existence results for a random fractional equation under a Carathéodory…”

“…Ntouyas [24]. The basic tool in the study of the problems for random fractional differential equations is to treat it as a fractional differential equation in some appropriate Banach space.…”

“…See for example, M. Benchohra, et al [2], J. Deng, et al [5] and the references therein. In this paper, inspired and motivated by Lupulescu et al [22][23][24][25] and Dhage [6][7][8][9], under the condition of the Lipschitzean right-hand side we obtain the existence and uniqueness of the solutions of the fractional random differential equations with delay. To prove this assertion we use an idea of successive approximations which has been applied in [21] for the fractional differential equations for this problem.…”