In this paper we present new types of pseudo-fractional integral and derivatives on a semiring \(([a,b],\oplus ,\odot )\). 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.

在本文中，我们介绍了半环\(([a,b],\oplus ,\odot )\)上的新型伪分数积分和导数。这些算子被称为\(\psi \) -Riemann-Liouville-Mittag-Leffler 伪分数积分和导数和\(\psi \) -Caputo-Mittag-Leffler 伪分数导数。讨论了一些性质，如半群定律、伪分数微分和伪分数积分算子之间的合成关系、伪分数导数之间的合成关系等。最后，作为一个应用，我们证明了分数阶微积分基本定理的两个版本。