**4. Conclusions**

We have examined the time-fractional heat conduction equation with the Caputo fractional derivative of the order 0 < *α* ≤ 2 in an infinite plane with two external half-infinite cracks whose surfaces are exposed to the heat flux loading. The solution has been obtained using the integral transform technique. Several special cases corresponding to the integer values of the order of the time-derivative have been considered.

**Author Contributions:** Both authors have equally contributed to this work. Both authors read and approved the final manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
