A new generalized Gronwall inequality with a double singularity and its applications to fractional stochastic differential equations. (English) Zbl 1472.34011
This paper focuses primarily on a new generalized Gronwall inequality with a double singularity and its applications to fractional stochastic differential equations
The first few pages introduce all the necessary notation and terminology to understand the paper: the theory of operators and ingenious techniques to investigate the well-posedness of mild solution to semilinear fractional stochastic differential equations is discussed.
The main results are presented in Section 3 (Generalized Gronwall inequalities with weakly singular kernels) with the help of Theorem 3.1 and 3.2. In Section 4, the properties and integral inequalities obtained in Section 3 to discuss the well-posedness of semilinear fractional stochastic differential equations are studied.
The first few pages introduce all the necessary notation and terminology to understand the paper: the theory of operators and ingenious techniques to investigate the well-posedness of mild solution to semilinear fractional stochastic differential equations is discussed.
The main results are presented in Section 3 (Generalized Gronwall inequalities with weakly singular kernels) with the help of Theorem 3.1 and 3.2. In Section 4, the properties and integral inequalities obtained in Section 3 to discuss the well-posedness of semilinear fractional stochastic differential equations are studied.
Reviewer: Arzu Ahmadova (Gazimağusa)
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34F05 | Ordinary differential equations and systems with randomness |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
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