Matematik Bölümü Yayın Koleksiyonu

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Now showing 1 - 10 of 107
  • Article
    Citation - Scopus: 4
    On Mild Solution of Abstract Neutral Fractional Order Impulsive Differential Equations With Infinite Delay
    (Eudoxus Press, LLC, 2018) Anguraj, A.; Baleanu, Dumitru; Kanjanadevi, S.; Baleanu, D.; Matematik
    We prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. © 2018 by Eudoxus Press, LLC. All rights reserved.
  • Article
    Citation - WoS: 7
    On Dynamics of Fractional-Order Model of Hcv Infection
    (Univ Prishtines, 2017) Khodabakhshi, Neda; Baleanu, Dumitru; Vaezpour, S. Mansour; Baleanu, Dumitru; Matematik
    In this paper, we investigate the dynamical behavior of the fractional-order model within Caputo derivative of HCV infection. Stability analysis of the equilibrium points is according to the basic reproduction number R-0. The numerical simulations are also presented to illustrate the results.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    Performance Evaluation of Matched Asymptotic Expansions for Fractional Differential Equations With Multi-Order
    (Soc Matematice Romania, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Sayevand, Khosro; Matematik
    An extension of the concept of the asymptotic expansions method is presented in this paper. The multi-order differential equations of fractional order are investigated and the convergence of the proposed method is proven. The reported results show that the present approach is very effective and accurate and also are in good agreement with the ones in the literature.
  • Article
    Citation - Scopus: 2
    Non-Integer Variable Order Dynamic Equations on Time Scales Involving Caputo-Fabrizio Type Differential Operator
    (Eudoxus Press, LLC, 2018) Baleanu, D.; Baleanu, Dumitru; Nategh, M.; Matematik
    This work deals with the conecept of a Caputo-Fabrizio type non-integer variable order differential opertor on time scales that involves a non-singular kernel. A measure theoretic discussion on the limit cases for the order of differentiation is presented. Then, corresponding to the fractional derivative, we discuss on an integral for constant and variable orders. Beside the obtaining solutions to some dynamic problems on time scales involving the proposed derivative, a fractional folrmulation for the viscoelastic oscillation problem is studied and its conversion into a third order dynamic equation is presented. © 2018 by Eudoxus Press, LLC. All rights reserved.
  • Article
    Citation - Scopus: 1
    A Lebesgue Integrable Space of Boehmians for a Class of Dk Transformations
    (Eudoxus Press, LLC, 2018) Al-Omari, S.; Baleanu, Dumitru; Baleanu, D.; Matematik
    Boehmians are objects obtained by an abstract algebraic construction similar to that of field of quotients and it in some cases just gives the field of quotients. As Boehmian spaces are represented by convolution quotients, integral transforms have a natural extension onto appropriately defined spaces of Boehmians. In this paper, we have defined convolution products and a class of delta sequences and have examined the axioms necessary for generating the Dk spaces of Boehmians. The extended Dk transformation has therefore been defined as a one-to-one onto mapping continuous with respect to Δ and δ convergences. Over and above, it has been asserted that the necessary and sufficient conditions for an integrable sequence to be in the range of the Dk transformation is that the class of quotients belongs to the range of the representative. Further results related to the inverse problem are also discussed. © 2018 EUDOXUS PRESS, LLC.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 7
    On Some Self-Adjoint Fractional Finite Difference Equations
    (Eudoxus Press, Llc, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; Salehi, Saeid; Matematik
    Recently, the existence of solution for the fractional self-adjoint equation Delta(nu)(nu-1) (p Delta y)(t) = h(t) for order 0 < nu <= 1 was reported in [9]. In this paper, we investigated the self-adjoint fractional finite difference equation Delta(nu)(nu-2)(p Delta u(t) = j(t,p(t+nu - 2)) via the boundary conditions y(nu - 2) = 0 , such that Delta y(nu - 2) = 0 and Delta y(nu+b) = 0. Also, we analyzed the self-adjoing fractional finite difference equation Delta(nu()(nu-2)p Delta(2)y)(t) = j(t,[(t+nu - 2)Delta(2)y(t+nu-3)) via the boundary conditions y(nu - 2) = 0, Delta y(nu - 2) = 0, Delta(2)y(nu - 2) = 0 and Delta 2y(nu+b) = 0. Finally, we conclude a result about the existence of solution for the general equation Delta(nu()(nu-2)p Delta(m)y)(t) = h(t,p(t+nu - m - 1)Delta(m)y(t+nu - m - 1)) via the boundary conditions y(nu - 2) = Delta y(nu - 2) = Delta(2)y(nu - 2) = center dot center dot center dot Delta(m)y(nu+b) = 0 for oder 1 < nu <= 2.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 8
    Psychometric Properties of the Turkish Version of Cohen- Mansfield Agitation Inventory in Patients With Dementia
    (Gunes Kitabevi Ltd Sti, 2012) Baştuğ, Gülbahar; Ozel-Kizil, E. Tugba; Bastug, Gulbahar; Erdogan, Seyda; Sakarya, Direnc; Durmaz, Nazli; Psikoloji
    Introduction: Cohen-Mansfield Agitation Inventory (CMAI) is frequently used in patients with dementia for the assessment of agitation severity. This instrument is especially used in research investigating the severity of behavioral symptoms and their treatment responses. In this study, psychometric properties of the Turkish version of CMAI were investigated in patients with dementia (n=52). Materials and Method: CMAI-Turkish version was applied by face-to-face interview to the caregivers of dementia patients who were admitted to a geriatric psychiatry outpatient clinic. For validity, the correlations between CMAI total scores and Neuropsychiatry Inventory (NPI) total and subscale scores were evaluated. For internal consistency, Cronbach alpha value of the items was calculated. Results: CMAI scores were significantly correlated with NPI scores and Cronbach alpha value of the scale was high (0.89). Conclusion: Turkish version of CMAI is a valid and reliable tool for the assessment of the frequency and severity of agitation behavior. Further studies might evaluate inter-rater reliability of the scale in inpatients with dementia.
  • Article
    Citation - WoS: 34
    Citation - Scopus: 30
    New Solutions of the Transport Equations in Porous Media Within Local Fractional Derivative
    (Editura Acad Romane, 2016) Zhang, Yu; Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; Matematik
    In this manuscript we use the series expansion method within local fractional derivative to obtain the solutions of both homogeneous and non-homogeneous transport equations. The new reported solutions are able to describe more efficiently the behavior of solutions of the transport phenomena in porous media.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 6
    A Fractional Derivative Inclusion Problem Via an Integral Boundary Condition
    (Eudoxus Press, Llc, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; Matematik
    We investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.
  • Article
    Citation - WoS: 9
    Analytic Study of Allen-Cahn Equation of Fractional Order
    (int Center Scientific Research & Studies, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; Matematik
    The key purpose of the present article is to analyze the Allen Cahn equation of fractional order. The fractional Allen-Cahn equation models the process of phase separation in iron alloys, along with order-disorder transitions. The analytical technique is employed to investigate the fractional model of Allen-Cahn equation. The numerical results are shown graphically. The outcomes show that the analytical technique is very efficient and user friendly for handling nonlinear fractional differential equations describing the real world problems.