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

By Aziz Khan, Hasib Khan, José Francisco Gómez‐Aguilar, Thabet Abdeljawad. Chaos, Solitons & Fractals, 2019

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Abstract 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.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/19205d08af71e38db586bda9f773e8ceb1f39b69