## Abstract

In this work, we study two final value problems for fractional reaction equation with standard Brownian motion W(t) and fractional Brownian motion B ^{H}(t), for [Formula presented]. Firstly, the well-posedness of each problem is investigated under strongly choices of data. We aim to find spaces where we obtain the existence of a unique solution of each problem, and establish some regularity results. Next, since the first problem and the second problem when [Formula presented] are ill-posed due to the lack of regularity of the terminal condition, a well-known regularization method called Fourier truncation is applied to construct regularized solutions. Furthermore, convergence results of regularized solutions are proposed.

Original language | English |
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Article number | 103158 |

Journal | Bulletin des Sciences Mathématiques |

Volume | 179 |

Early online date | 3 Jun 2022 |

DOIs | |

Publication status | Published - 1 Oct 2022 |

## Keywords

- Fractional Brownian motion
- Fractional differential equation
- Fractional reaction equation
- Ill-posedness
- Inverse problem
- Well–posedness