An algebraic derivative associated to the operator ${\displaystyle D^{\delta }}$

In this paper we get an algebraic derivative relative to the convolution ${\displaystyle (f\cdot g)\left(t\right)={\int }_0^{t}if(t-\psi )g(\psi )d\psi }$ associated to the operator ${\displaystyle D^{\delta }}$, 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