Is expiation by fasting obligatory for one who caused the death of a Muslim woman with his car as a result of a road accident, knowing that the deceased's family has forgiven him and accepted a sum of money that is not equivalent to the blood money (diyah)?

What happened to the woman is considered accidental killing (manslaughter), because the speed at which you were driving reached an uncontrollable limit, and the accident could have been avoided had the speed been normal. It is the driver's duty not to exceed the limit that allows him to maintain control of his vehicle.

Accidental killing entails two consequences: 1. Expiation (Kaffarah): Freeing a believing slave, or fasting for two consecutive months for whoever does not find a slave to free. 2. Blood Money (Diyah): The woman's blood money is to be paid by your 'Aqilah (male relatives responsible for paying blood money), unless her guardians (Awliya' al-Dam) waive it, based on the words of Allah Almighty: "And whoever kills a believer by mistake - then the freeing of a believing slave and a compensation (blood money) to be handed over to his family, unless they (in charity) forgo it. But if he was from a people hostile to you and he was a believer, then the freeing of a believing slave [is sufficient]. And if he was from a people with whom you have a treaty, then a compensation (blood money) to be handed over to his family and the freeing of a believing slave. And he who finds no [slave to free] - then a fast for two consecutive months as repentance to Allah. And ever is Allah Knowing and Wise."