  We survey methods and results of fractional differential equations in which
an unknown function is under the operation of integration and/or
differentiation of fractional order. As an illustrative example, we review
results on fractional integral and differential equations of thermistor type.
Several nonlocal problems are considered: with Riemann-Liouville, Caputo, and
time-scale fractional operators. Existence and uniqueness of positive solutions
are obtained through suitable fixed-point theorems in proper Banach spaces.
Additionally, existence and continuation theorems are given, ensuring global
existence.
