Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel.

• Discussing the Hyers-Ulam stability for nonlinear differential equations involving Atangana-Baleanu fractional derivatives. • Fractional differential equations with singularity and nonlinear p-Laplacian operator in Banach's space are studied. • Guo-Krasnoselskii theorem was consider to obtain the results. In this paper we are established the existence of positive solutions (EPS) and the Hyers-Ulam (HU) stability of a general class of nonlinear Atangana-Baleanu-Caputo (ABC) fractional differential equations (FDEs) with singularity and nonlinear p -Laplacian operator in Banach's space. To find the solution for the EPS, we use the Guo-Krasnoselskii theorem. The fractional differential equation is converted into an alternative integral structure using the Atangana-Baleanu fractional integral operator. Also, HU-stability is analyzed. We include an example with specific parameters and assumptions to show the results of the proposal. [ABSTRACT FROM AUTHOR]