An algebraic derivative associated to the operator $D^δ$

In this paper we get an algebraic derivative relative to the convolution $(f*g) (t)=∫_0^ti f(t-ψ)g(ψ)dψ$ associated to the operator $D^δ$, which is used, together with the corresponding operational calculus, to solve an integral-differential equation. Moreover we show a certain convolution property for the solution of that equation