Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Mohammadi, HakimehSubject: search.filters.subject.Boundary Value Problem

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 15
    Citation - Scopus: 14
    Criteria for Existence of Solutions for a Liouville-Caputo Boundary Value Problem Via Generalized Gronwall's Inequality
    (Springer, 2021) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; Mohammadi, Hakimeh
    In this research, we first investigate the existence of solutions for a new fractional boundary value problem in the Liouville-Caputo setting with mixed integro-derivative boundary conditions. To do this, Kuratowski's measure of noncompactness and Sadovskii's fixed point theorem are our tools to reach this aim. In the sequel, we discuss the continuous dependence of solutions on parameters by means of the generalized Gronwall inequality. Moreover, we consider an inclusion version of the given boundary problem in which we study its existence results by means of the endpoint theory. Finally, we prepare two simulative numerical examples to confirm the validity of the analytical findings.
  • Article
    Citation - WoS: 117
    Citation - Scopus: 120
    A Novel Modeling of Boundary Value Problems on the Glucose Graph
    (Elsevier, 2021) Etemad, Sina; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
    In this article, with due attention to a new labeling method for vertices of arbitrary graphs, we investigate the existence results for a novel modeling of the fractional multi term boundary value problems on each edge of the graph representation of the Glucose molecule. In this direction, we consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of the Glucose molecule and then derive some existence results by applying two known fixed point theorems. Finally, we provide an example to illustrate the validity of our main result. (c) 2021 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 60
    Citation - Scopus: 65
    The Existence of Solutions for a Nonlinear Mixed Problem of Singular Fractional Differential Equations
    (Springer, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
    By using fixed point results on cones, we study the existence of solutions for the singular nonlinear fractional boundary value problem (c)D(alpha)u(t) = f(t, u(t), u'(t), (c)D(beta)u(t)), u(0) = au(1), u'(0) = b(c)D(beta)u(1), u ''(0) = u'''(0) = u((n-1))(0) = 0, where n >= 3 is an integer, alpha is an element of (n - 1, n), 0 < beta < 1, 0 < a < 1, 0 < b < Gamma (2 - beta), f is an L-q-Caratheodory function, q > 1/alpha-1 and f(t,x,y,z) may be singular at value 0 in one dimension of its space variables x, y, z. Here, D-c stands for the Caputo fractional derivative.