Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Baleanu, DumitruPublisher: search.filters.publisher.Univ Nis, Fac Sci Math

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Fractional Differential Equation With a Complex Potential
    (Univ Nis, Fac Sci Math, 2020) Ugurlu, Ekin; Tas, Kenan; Baleanu, Dumitru
    In this manuscript, we discuss the square-integrable property of a fractional differential equation having a complex-valued potential function and we show that at least one of the linearly independent solutions of the fractional differential equation must be squarely integrable with respect to some function containing the imaginary parts of the spectral parameter and the potential function.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Approximate Controllability of Second-Order Nonlocal Impulsive Partial Functional Integro-Differential Evolution Systems
    (Univ Nis, Fac Sci Math, 2019) Kavitha, Velusamy; Baleanu, Dumitru; Arjunan, Mani Mallika; Nagaraj, Mahalingam
    This manuscript is involved with a class of second-order impulsive partial functional integro-differential evolution equations with nonlocal conditions in Banach spaces. Sufficient conditions ensuring the existence and approximate controllability of mild solutions are established. Theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem are employed for achieving the required results. An example is analyzed to illustrate the effectiveness of the outcome.
  • Conference Object
    Citation - WoS: 38
    Citation - Scopus: 48
    Analysis of Keller-Segel Model With Atangana-Baleanu Fractional Derivative
    (Univ Nis, Fac Sci Math, 2018) Baleanu, Dumitru; Celik, Ercan; Dokuyucu, Mustafa Ali
    The new definition of the fractional derivative was defined by Atangana and Baleanu in 2016. They used the generalized Mittag-Leffler function with the non-singular and non-local kernel. Further, their version provides all properties of fractional derivatives. Our aim is to analyse the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative in Caputo sense. Using fixed point theory, we first show the existence of coupled solutions. We then examine the uniqueness of these solutions. Finally, we compare our results numerically by modifying our model according to both definitions, and we demonstrate these results on the graphs in detail. All computations were done using Mathematica.
  • Article
    Citation - WoS: 16
    Citation - Scopus: 15
    On a New Definition of Fractional Differintegrals With Mittag-Leffler Kernel
    (Univ Nis, Fac Sci Math, 2019) Baleanu, Dumitru; Fernandez, Arran
    We introduce a new family of fractional differential and integral operators which emerge from a fractional iteration process applied to some existing fractional operators with Mittag-Leffler kernels. We analyse the new operators and prove various facts about them, including a semigroup property. We also solve some ODEs in this new model by using Laplace transforms, and discuss applications of our results.