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  • Lyapunov-type inequalities for mixed non-linear forced differential equations within conformable derivatives 

    Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Özbekler, Abdullah (Springer, 2018-06-20)
    We state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + ...
  • On square integrable solutions of a fractional differential equation 

    Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan (Elsevier Science Bv, 2018-11-15)
    In this paper we construct the Weyl-Titchmarsh theory for the fractional Sturm-Liouville equation. For this purpose we used the Caputo and Riemann-Liouville fractional operators having the order is between zero and one.
  • Some fixed point results for TAC-type contractive mappings 

    Chandok, Sumit; Taş, Kenan; Ansari, Arslan Hojat (Hindawi Publishing Corporation, 2016)
    We prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results ...
  • On dilation, scattering and spectral theory for two-interval singular differential operators 

    Allahverdiev, Bilender P.; Uğurlu, Ekin (Soc Matematice Romania, 2015)
    This paper aims to construct a space of boundary values for minimal symmetric singular impulsive-like Sturm-Liouville (SL) operator in limit-circle case at singular end points a, b and regular inner point c. For this purpose ...
  • Fuzzy prediction strategies for gene-environment networks - fuzzy regression analysis for two-modal regulatory systems 

    Kropat, Erik; Özmen, Ayşe; Weber, Gerhard-Wilhelm; Meyer-Nieberg, Silja; Defterli, Özlem (EDP Sciences, 2016-04)
    Target-environment networks provide a conceptual framework for the analysis and prediction of complex regulatory systems such as genetic networks, eco-finance networks or sensor-target assignments. These evolving networks ...
  • Spectral analysis of the direct sum hamiltonian operators 

    Allahverdiev, Bilender P.; Uğurlu, Ekin (Natl Inquiry Services Centre, 2016-10)
    In this paper we investigate the deficiency indices theory and the selfad-joint and nonselfadjoint (dissipative, accumulative) extensions of the minimal symmetric direct sum Hamiltonian operators. In particular using the ...
  • The quaternion group has ghost number three 

    Aksu Altunbulak, Fatma; Green, David J. (Academic Press Inc Elsevier Science, 2017-01-01)
    We prove that the group algebra of the quaternion group Q(8) over any field of characteristic two has ghost number three.
  • Regular fractional dissipative boundary value problems 

    Baleanu, Dumitru; Uğurlu, Ekin (Springer, 2016-07-01)
    In this manuscript we present a regular dissipative fractional operator associated with a fractional boundary value problem. In particular, we present two main dissipative boundary value problems and one of them contains ...
  • Regular fractional differential equations in the sobolev space 

    Uğurlu, Ekin; Baleanu, Dumitru; Taş, Kenan (Walter De Gruyter GMBH, 2017-06)
    In this paper regular fractional Sturm-Liouville boundary value problems are considered. In particular, new inner products are described in the Sobolev space and a symmetric operator is established in this space.
  • The spectral analysis of a nuclear resolvent operator associated with a second order dissipative differential operator 

    Uğurlu, Ekin; Bairamov, Elgiz (Springer, 2017-06)
    In this paper, we introduce a new approach for the spectral analysis of a linear second order dissipative differential operator with distributional potentials. This approach is related with the inverse operator. We show ...
  • Dirac systems with regular and singular transmission effects 

    Uğurlu, Ekin (Scientific Technical Research Council Turkey-TUBİTAK, 2017)
    In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl's limit-circle case with finite transmission conditions. In particular, these transmission conditions ...
  • An algorithm for Hopf bifurcation analysis of a delayed reaction-diffusion model 

    Kayan, Şeyma; Merdan, H. (Springer, 2017-07)
    We present an algorithm for determining the existence of a Hopf bifurcation of a system of delayed reaction-diffusion equations with the Neumann boundary conditions. The conditions on parameters of the system that a Hopf ...
  • On a new class of fractional operators 

    Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, Dumitru (Springer, 2017-08-22)
    This manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems ...
  • Singular left-definite Hamiltonian systems in the Sobolev space 

    Uğurlu, Ekin; Taş, Kenan; Baleanu, Dumitru (INT Scientific Research Publications, 2017-08)
    This paper is devoted to construct Weyl's theory for the singular left-definite even-order Hamiltonian systems in the corresponding Sobolev space. In particular, it is proved that there exist at least n-linearly independent ...
  • Singular Dirac systems in the Sobolev space 

    Uğurlu, Ekin (Scientific Technical Research Council Turkey-TUBİTAK, 2017)
    In this paper we construct Weyl's theory for the singular left-definite Dirac systems. In particular, we prove that there exists at least one solution of the system of equations that lies in the Sobolev space. Moreover, ...
  • A generalized Lyapunov-type inequality in the frame of conformable derivatives 

    Abdeljawad, Thabet; Alzabut, Jehad; Jarad, Fahd (Springer, 2017-10-11)
    We prove a generalized Lyapunov-type inequality for a conformable boundary value problem (BVP) of order alpha is an element of (1, 2]. Indeed, it is shown that if the boundary value problem (T(alpha)(c)x)(t) + r(t) x(t) ...
  • Dissipative operator and its Cayley transform 

    Uğurlu, Ekin; Taş, Kenan (Scientific Technical Research Council Turkey-TUBİTAK, 2017)
    In this paper, we investigate the spectral properties of the maximal dissipative extension of the minimal symmetric differential operator generated by a second order differential expression and dissipative and eigenparameter ...
  • Singular multiparameter dynamic equations with distributional potentials on time scales 

    Uğurlu, Ekin (Natl Inquiry Services Centre, 2017)
    In this paper, we consider both singular single and several multiparameter second order dynamic equations with distributional potentials on semi-infinite time scales. At first we construct Weyls theory for the single ...
  • Some results on predator-prey dynamic systems with beddington-deangelis type functional response on time scale calculus 

    Pelen, Neslihan Nesliye; Güvenilir, Ayşe Feza; Kaymakçalan, Billur (Dynamic Publishers, 2017-03)
    We consider two dimensional predator-prey system with Beddington-DeAngelis type functional response on time scales. For this special case, we try to find under which conditions the system is permanent and globally attractive. ...
  • Bifurcation analysis of a modified tumor-immune system interaction model involving time delay 

    Kayan, Şeyma; Merdan, H.; Yafia, R.; Göktepe, S. (EDP Sciences, 2017)
    We study stability and Hopf bifurcation analysis of a model that refers to the competition between the immune system and an aggressive host such as a tumor. The model which describes this competition is governed by a ...

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