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Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Publisher: search.filters.publisher.MdpiSubject: search.filters.subject.Atangana-Baleanu Fractional Derivative

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  • Article
    Citation - WoS: 7
    Citation - Scopus: 9
    Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators
    (Mdpi, 2020) Darzi, Rahmat; Agheli, Bahram; Baleanu, Dumitru
    A new form of nonlinear Langevin equation (NLE), featuring two derivatives of non-integer orders, is studied in this research. An existence conclusion due to the nonlinear alternative of Leray-Schauder type (LSN) for the solution is offered first and, following that, the uniqueness of solution using Banach contraction principle (BCP) is demonstrated. Eventually, the derivatives of non-integer orders are elaborated in Atangana-Baleanu sense.
  • Article
    Citation - WoS: 51
    Citation - Scopus: 88
    Chaos in a Cancer Model Via Fractional Derivatives With Exponential Decay and Mittag-Leffler Law
    (Mdpi, 2017) Guadalupe Lopez-Lopez, Maria; Manuel Alvarado-Martinez, Victor; Baleanu, Dumitru; Khan, Hasib; Francisco Gomez-Aguilar, Jose; Alvarado-Martínez, Victor Manuel; Gómez-Aguilar, José Francisco; López-López, María Guadalupe
    In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.