Browsing by Author "Khalili, Yasser"

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Citation Count: Khalili, Y.; Baleanu, D., "A Uniqueness Result for Differential Pencils With Discontinuities From İnterior Spectral Data", Analysis (Germany), Vol. 38, No. 4, pp. 195-202, (2018).
A Uniqueness Result for Differential Pencils With Discontinuities From İnterior Spectral Data
(De Gruyter Open LTD, 2018) Khalili, Yasser; Baleanu, Dumitru; 56389
In this work, the interior spectral data is employed to study the inverse problem for a differential pencil with a discontinuity on the half line. By using a set of values of the eigenfunctions at some internal point and eigenvalues, we obtain the functions q0(x) and q1(x) applied in the diffusion operator.
Citation Count: Khalili, Y.; Baleanu, D., "Determination of An Impulsive Diffusion Operator From Interior Spectral Data", Analysis (Germany), Vol. 40, No. 1, pp. 39-45, (2020).
Determination of An Impulsive Diffusion Operator From Interior Spectral Data
(De Gruyter Open LTD, 2020) Khalili, Yasser; Baleanu, Dumitru; 56389
In the present work, the interior spectral data is used to investigate the inverse problem for a diffusion operator with an impulse on the half line. We show that the potential functions q0(x) and q1 (x) can be uniquely established by taking a set of values of the eigenfunctions at some internal point and one spectrum.
Citation Count: Khalili, Yasser; Kadkhoda, Nematollah; Baleanu, Dumitru, "Inverse problems for the impulsive Sturm-Liouville operator with jump conditions", Inverse Problems in Science and Engineering, Vol. 27, No. 10, pp. 1442-1450, (2019).
Inverse problems for the impulsive Sturm-Liouville operator with jump conditions
(Taylor&Francis LTD, 2019) Khalili, Yasser; Kadkhoda, Nematollah; Baleanu, Dumitru; 56389
The inverse problem for impulsive Sturm-Liouville operators with discontinuity conditions is considered. We have shown that all parameters used in the boundary conditions as well as can be uniquely established by a set of values of eigenfunctions at the mid-point and one spectrum. Moreover, we discuss Gesztesy-Simon theorem and show that if the potential function is prescribed on the interval for some , then parts of a finite number of spectra suffice to determine on .
Citation Count: Khalili, Yasser; Kadkhoda, Nematollah; Baleanu, Dumitru (2020). "On the determination of the impulsive Sturm-Liouville operator with the eigenparameter-dependent boundary conditions", Mathematical Methods in the Applied Sciences, Vol. 43, No. 11, pp. 7143-7151.
On the determination of the impulsive Sturm-Liouville operator with the eigenparameter-dependent boundary conditions
(2020) Khalili, Yasser; Kadkhoda, Nematollah; Baleanu, Dumitru; 56389
In the present work, we consider the inverse problem for the impulsive Sturm-Liouville equations with eigenparameter-dependent boundary conditions on the whole interval (0,pi) from interior spectral data. We prove two uniqueness theorems on the potential q(x) and boundary conditions for the interior inverse problem, and using the Weyl function technique, we show that if coefficients of the first boundary condition, that is, h(1),h(2), are known, then the potential function q(x) and coefficients of the second boundary condition, that is, H-1,H-2, are uniquely determined by information about the eigenfunctions at the midpoint of the interval and one spectrum or partial information on the eigenfunctions at some internal points and some of two spectra.
Citation Count: Khalili, Yasser; Baleanu, Dumitru (2020). "Recovering differential pencils with spectral boundary conditions and spectral jump conditions", Journal of Inequalities and Applications, Vol. 2020, No. 1.
Recovering differential pencils with spectral boundary conditions and spectral jump conditions
(2020) Khalili, Yasser; Baleanu, Dumitru; 56389
In this work, we discuss the inverse problem for second order differential pencils with boundary and jump conditions dependent on the spectral parameter. We establish the following uniqueness theorems: (i) the potentials qk(x) and boundary conditions of such a problem can be uniquely established by some information on eigenfunctions at some internal point b∈(π2,π) and parts of two spectra; (ii) if one boundary condition and the potentials qk(x) are prescribed on the interval [π/ 2 (1 − α) , π] for some α∈ (0 , 1) , then parts of spectra S⊆ σ(L) are enough to determine the potentials qk(x) on the whole interval [0 , π] and another boundary condition.