Existence and Uniqueness of Abstract Stochastic Fractional-Order Differential Equation

In this paper, the existence and uniqueness about the solution for a class of abstract stochastic fractional-order differential equations                                           where  in and  are given functions, are investigated, where the fractional derivative is described in Caputo sense. The fractional calculus, stochastic analysis techniques and the standard $Picard's$ iteration method are used to obtain the required

A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition

In this paper, we shall discuss the uniqueness ”pathwise uniqueness” of the solutions of stochastic partial differential equations (SPDEs) with non-local initial condition,We shall use the Yamada-Watanabe condition for ”pathwise uniqueness” of the solutions of the stochastic differential equation; this condition is weaker than the usual Lipschitz condition. The proof is based on Bihari’sinequality

A Parabolic Transform and Averaging Methods for General Partial Differential Equations

Averaging method of the fractional general partial differential equations and a special case of these equations are studied, without any restrictions on the characteristic forms of the partial differential operators. We use the parabolic transform, existence and stability results can be obtained

Initial Value Problem for Stochastic Hyprid Hadamard Fractional Differential Equation: Hyprid Hadamard

In this paper, we discuss the existence of solutions for a stochastic initial value problem of Hyprid fractional dierential equations of Hadamard type given by                            where HD is the Hadamard fractional derivative, and is the Hadamard fractional integral and be such that are investigated. The fractional calculus and stochastic analysis techniques are used to obtain the required results.&nbsp