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

Aziz Khan, Hasib Khan, J.F. Gómez-Aguilar and Thabet Abdeljawad

Chaos, Solitons & Fractals, 2019, vol. 127, issue C, 422-427

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.

Keywords: ABC-fractional differential equation; p-Laplacian operator; Green’s function; Unique solution (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:127:y:2019:i:c:p:422-427

DOI: 10.1016/j.chaos.2019.07.026

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