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Let E be the set of integrable and derivable causal functions of x defined onthe real interval I from a to infinity, a being real, such f(a) is equal tozero for x lower than or equal to a. We give the expression of one operatorthat yields the integral operator and derivative operators of the function f atany s-order. For s positive integer real number, we obtain the ordinarys-iterated integral of f. For s negative integer real number we obtain the|s|-order ordinary derivatives of f. Any s positive real or positive real partof s complex number corresponds to s-integral operator of f. Any s negativereal number or negative real part of s complex number corresponds to |s|-orderderivative operator of f. The results are applied for f being a monom. Andremarkable relations concerning the e and {\pi} order integrals and e and {\pi}order derivatives are given, for e and {\pi} transcendental numbers. Similarresults may also be obtained for anticausal functions. For particular values ofa and s, the operator gives exactly Liouville fractional integral, Riemannfractional integral, Caputo fractional derivative, Liouville-Caputo fractionalderivative. Finally, the new operator is neither integral nor derivativeoperator. It is integral and derivative operators at the same time. It deservesof being named:raoelinian operator is proposed.

A new operator giving integrals and derivatives operators for any order at the same time