ψ-Mittag-Leffler pseudo-fractional operators

In this paper we present new types of pseudo-fractional integral and derivatives on a semiring ([a, b], circle plus, circle dot). These operators are called the psi-Riemann-Liouville-Mittag-Leffler pseudo-fractional integrals and derivatives and psi-Caputo-Mittag-Leffler pseudo-fractional derivatives. Some properties, like the semigroup law, composition relations between pseudo-fractional differentiation and pseudo-fractional integration operators, composition relations between pseudo-fractional derivatives, among others, are discussed. Finally, as an application, we proved two versions of the fundamental theorem of fractional calculus.