ABSTRACT FRACTIONAL DIFFERENTIAL INCLUSIONS WITH GENERALIZED LAPLACE DERIVATIVES

In this paper, we use the vector-valued Laplace transform to introduce and systematically analyze the notion of a generalized Laplace fractional derivative. The abstract fractional differential inclusions with generalized Laplace derivatives are investigated with the help of our recent results about \(\varvec{(F,G,C)}\) $\mathbf{(}\mathit{F}\mathbf{,}\mathit{G}\mathbf{,}\mathit{C}\mathbf{)}$ -regularized resolvent operator families subgenerated by multivalued linear operators. Especially, we consider the abstract fractional differential inclusions with generalized Hilfer \(\varvec{(a,b,\alpha )}\) $\mathbf{(}\mathit{a}\mathbf{,}\mathit{b}\mathbf{,}\mathit{\alpha }\mathbf{)}$ -derivatives and Prabhakar derivatives.