On right fractional calculus

Abstract

Here are presented fractional Taylor type formulae with fractional integral remainder and fractional differential formulae, regarding the right Caputo fractional derivative, the right generalized fractional derivative of Canavati type [Canavati JA. The Riemann–Liouville integral. Nieuw Archief Voor Wiskunde 1987;5(1):53–75] and their corresponding right fractional integrals. Then are given representation formulae of functions as fractional integrals of their above fractional derivatives, as well as of their right and left Weyl fractional derivatives. At the end, we mention some far reaching implications of our theory to mathematical analysis computational methods. Also we compare the right Caputo fractional derivative to right Riemann–Liouville fractional derivative.