Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel. (October 2019)

• Record Type: Journal Article
• Authors: Khan, Aziz; Khan, Hasib; Gómez-Aguilar, J.F.; Abdeljawad, Thabet
• Is Part Of: Chaos, solitons and fractals. Volume 127(2019)
• Page Start: 422
• Page End: 427
• Publication Date: 2019-10
• Subjects: ABC-fractional differential equation -- p-Laplacian operator -- Green's function -- Unique solution; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.07.026
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: 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. 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.