Is it permissible to pay a fidya for 40 days of missed fasting due to illness and the difficulty of making them up, and what is the value of the fidya?

If the illness you are suffering from is hoped to be cured, then it is not permissible for you to switch from making up the fasts (qada') to feeding the poor (fidya). You can make up the days non-consecutively. However, if your illness is not hoped to be cured and causes you severe hardship in fasting, then it is permissible for you to feed a poor person for each day. The amount of feeding is one mudd of food (approximately 750 grams of rice) or half a saa' of other food (approximately 1.5 kilograms). The trusted physician is the reference for determining the type of illness. Childcare or potential hardship are not considered excuses that permit switching from making up the fasts to feeding the poor.