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, HakimehScopus Q: search.filters.scopusQuartile.Q1

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  • Article
    Citation - WoS: 124
    Citation - Scopus: 140
    On Modelling of Epidemic Childhood Diseases With the Caputo-Fabrizio Derivative by Using the Laplace Adomian Decomposition Method
    (Elsevier, 2020) Aydogn, Seher Melike; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
    We present a fractional-order epidemic model for childhood diseases with the new fractional derivative approach proposed by Caputo and Fabrizio. By applying the Laplace Adomian decomposition method (LADM), we solve the problem and the solutions are presented as infinite series converging to the solution. We prove the existence, uniqueness, and stability of the solution by using the fixed point theory. Also, we provide some numerical results to illustrate the effectiveness of the new derivative. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
  • 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: 716
    Citation - Scopus: 762
    A New Study on the Mathematical Modelling of Human Liver With Caputo-Fabrizio Fractional Derivative
    (Pergamon-elsevier Science Ltd, 2020) Jajarmi, Amin; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
    In this research, we aim to propose a new fractional model for human liver involving Caputo-Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard-Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives. (C) 2020 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 66
    Citation - Scopus: 74
    Two Fractional Derivative Inclusion Problems Via Integral Boundary Condition
    (Elsevier Science inc, 2015) Baleanu, Dumitru; Hedayati, Vahid; Rezapour, Shahram; Agarwal, Ravi P.; Moghaddam, Mehdi; Mohammadi, Hakimeh
    The goal of the manuscript is to analyze the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t), (c)D(beta)x(t)) with the boundary value conditions x(0) = 0 and x(1) + x'(1) = integral(eta)(0) x(s)ds, such that 0 < eta < 1, 1 < q <= 2, 0 < beta < 1 and q = beta > 1. Also, we investigate the existence of solutions for the Caputo fractional differential inclusion (c)D(q)x(t) is an element of F(t,x(t)) such that x(0) = a integral(nu)(0) x(s)ds and x(1) = b integral(eta)(0) x(s)ds, where 0 < nu, eta < 1, 1 < q <= 2 and a, b is an element of R. (C) 2014 Elsevier Inc. All rights reserved.
  • Article
    Citation - WoS: 217
    Citation - Scopus: 229
    Some Existence Results on Nonlinear Fractional Differential Equations
    (Royal Soc, 2013) Rezapour, Shahram; Mohammadi, Hakimeh; Baleanu, Dumitru
    In this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(alpha)u(t) = f(t, u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0) = u(T), and the three-point boundary condition u(0)= beta(1)u(eta) and u(T) = beta(2)u(eta), where T > 0, t is an element of I = [0, T], 0 < alpha < 1, 0 < eta < T, 0 < beta(1) < beta(2) < 1.