TR Dizin İndeksli Yayınlar Koleksiyonu / TR Dizin Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14365/4

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Author: search.filters.author.Sezer, MehmetScopus Q: search.filters.scopusQuartile.Q2

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  • Article
    Citation - WoS: 11
    Citation - Scopus: 11
    A Novel Graph-Operational Matrix Method for Solving Multidelay Fractional Differential Equations With Variable Coefficients and a Numerical Comparative Survey of Fractional Derivative Types
    (Scientific Technical Research Council Turkey-Tubitak, 2019-01-18) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet
    In this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 15
    Legendre Wavelet Solution of Neutral Differential Equations With Proportional Delays
    (Springer Heidelberg, 2019-04-01) Gumgum, Sevin; Ersoy Özdek, Demet; Özaltun, Gökçe; Bildik, Necdet; Özdek, Demet Ersoy; Kürkçü, Ömür Kıvanç; Sezer, Mehmet; Savaşaneril, Nurcan Baykuş
    The aim of this paper is to solve neutral differential equations with proportional delays by using Legendre wavelet method. Using orthonormal polynomials is the main advantage of this method since it enables a decrease in the computational cost and runtime. Some examples are displayed to illustrate the efficiency and accuracy of the proposed method. Numerical results are compared with various numerical methods in literature and show that the present method is very effectual in solving neutral differential equations with proportional delays.