On Stability, Boundedness and Square Integrability For A Kind Of Third Order Neutral Delay Differential Equations

Moulai-Khatir, Anes; Remili, Moussadek; Beldjerd, Djamila

doi:10.1109/icmit47780.2020.9047031

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2021

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“…Some researchers also worked on COVID-19 model with the help of fractional calculus [ 3 , 4 ]. On the other hand, fixed point theory helps much in the development of the qualitative and computational concepts of FDEs and their related dynamic equations [ 5 – 11 ]. But still no fixed definition of fractional operators has been defined.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative

et al. 2021

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Some fundamental conditions and hypotheses are established to ensure the existence, uniqueness, and stability to a class of implicit boundary value problems (BVPs) with Atangana–Baleanu–Caputo type derivative and integral. The required results are established by utilizing the Banach contraction mapping principle and fixed point theorem of Krasnoselskii. In addition, various types of stability results including Hyers–Ulam, generalized Hyers–Ulam, Hyers–Ulam–Rassias, and generalized Hyers–Ulam–Rassias stability are formulated for the problem under consideration. Pertinent examples are given to justify the results we obtain.

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