Abstract1.1. What is fractional calculus?1.2. Some prerequisite special functions1.3. Riemann–Liouville fractional differentiation1.4. Caputo fractional derivative1.5. Grünwald–Letnikov derivative1.6. Caputo–Fabrizio fractional differentiation1.7. The Atangana–Baleanu fractional derivative and integral1.8. Riesz fractional derivatives1.9. The Atangana–Gómez fractional derivative1.10. General fractional derivatives1.11. Fractal-fractional operatorsReferences