Importance of Riemann-Liouville fractional derivative from historical point of view

Question

Why Riemann-Liouville fractional derivative is important from historical point of view than that of Caputo fractional derivative? As we know Riemann-Liouville fractional derivative is more theoretical rather than practicability of Caputo fractional derivative. So better we establish properties for R-L fractional derivative and apply it Caputo one, is it correct approach?

Answer 1

Probably the most frequently used definition of fractional derivative and integral is due to B. Riemann and J. Liouville, commonly known as the Riemann-Liouville fractional derivative (integral). But in some situations, this approach is not useful due to lack of physical interpretation of initial and boundary conditions involving fractional derivatives, and also the Riemann-Liouville approach may yield derivative of a constant different from zero. A useful alternative to Riemann-Liouville derivative is the Caputo fractional derivative, introduced by M. Caputo in 1967 and adopted by Caputo and Mainardi 1969 in the context of the theory of viscoelasticity. Fractional derivatives are non–local in nature.