Does feeling a shiver as a result of thinking about sex while fasting invalidate the fast, and is expiation obligatory for the three days on which this occurred, and does thinking without a shiver nullify the fast?

Fasting is not invalidated merely by thinking about things that arouse desire, even if semen is discharged as a result, according to the majority of scholars, in contrast to Malik. This is the fatwa (definition) we adhere to. Therefore, merely feeling a tremor or merely thinking does not invalidate the fast. It is advisable to fear Allah and beware of following the footsteps of Satan, which may lead to forbidden acts, as Allah Almighty says: "O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing."