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Solar power manger best component selection

hi, i need to arrange the correct component selection for a power and solar-charge (Li-Ion Battery) system manager;

  • it will be a portable device (outdoor) that will work only a few hours (about 200 mA) of the day and the others (in low power mode 0.5 mA) can be charged in the sun;
  • the identified battery to be charged is a single cell 3.6V of 3100 mAh which can be charged at 4.2 (+-1%) (or similar)
  • the device should consume a minimum of 3 mA and a maximum of 200 mA, with some (small) peaks of 2A in case of maximum transmission (it is a GPRS/LTE radio);
  • the solar panel could be a 3.5V-16.2mA (vope-lope) 62 mW (4.2V-14.7mA) - or similar

regards

Gianluca