Matematik Bölümü Yayın Koleksiyonu

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

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Department: search.filters.department.Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüPublication Index: search.filters.publicationIndex.WoS

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Now showing 1 - 10 of 26
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme
    (Amer Inst Mathematical Sciences-AIMS, 2022) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem
    In the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.
  • Article
    Citation - WoS: 13
    Citation - Scopus: 17
    Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation
    (Springer, 2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru
    This work establishes the lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the Hirota bilinear method, as well as the robust integration techniques tanh-coth expansion and rational sine-cosine, to provide such innovative solutions. In order to explain specific physical difficulties, innovative lump periodic and analytical solutions have been investigated. These discoveries have been proven to be useful in the transmission of long-wave and high-power communications networks. It is important to highlight that the results given in thiswork depict new features and reflect previously unknown physical dynamics for the governing model.
  • Conference Object
    Citation - Scopus: 1
    Fractional Order Computing and Modeling with Portending Complex Fit Real-World Data
    (Springer International Publishing AG, 2023) Karaca, Yeliz; Rahman, Mati ur; Baleanu, Dumitru
    Fractional computing models identify the states of different systems with a focus on formulating fractional order compartment models through the consideration of differential equations based on the underlying stochastic processes. Thus, a systematic approach to address and ensure predictive accuracy allows that the model remains physically reasonable at all times, providing a convenient interpretation and feasible design regarding all the parameters of the model. Towards these manifolding processes, this study aims to introduce new concepts of fractional calculus that manifest crossover effects in dynamical models. Piecewise global fractional derivatives in sense of Caputo and Atangana-Baleanu-Caputo (ABC) have been utilized, and they are applied to formulate the Zika Virus (ZV) disease model. To have a predictive analysis of the behavior of the model, the domain is subsequently split into two subintervals and the piecewise behavior is investigated. Afterwards, the fixed point theory of Schauder and Banach is benefited from to prove the existence and uniqueness of at least one solution in both senses for the considered problem. As for the numerical simulations as per the data, Newton interpolation formula has been modified and extended for the considered nonlinear system. Finally, graphical presentations and illustrative examples based on the data for various compartments of the systems have been presented with respect to the applicable real-world data for different fractional orders. Based on the impact of fractional order reducing the abrupt changes, the results obtained from the study demonstrate and also validate that increasing the fractional order brings about a greater crossover effect, which is obvious from the observed data, which is critical for the effective management and control of abrupt changes like infectious diseases, viruses, among many more unexpected phenomena in chaotic, uncertain and transient circumstances.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 18
    Analysis of the family of integral equation involving incomplete types of I and Ī-functions
    (Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil Dutt
    The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.
  • Article
    Citation - Scopus: 1
    Remarks On Some Generalizations Of θ-Contraction
    (Univ Politehnica Bucharest, Sci Bull, 2023) Karapınar, Erdal; Cvetkovic, Marija
    The concept of θ-contraction was modified and generalized in several ways during the last decade. Some assumptions concerning the class Θ are shown to be super-fluous in order to obtain a unique fixed point for a θ-type contraction, θ-Suzuki type and, consequently, θ-contraction. Improvement of several previously published results are de-rived with a modified contractive condition and we have presented an example of possible application. The same approach was used for the F-Suzuki contraction and numerous generalizations are made.
  • Article
    Chain and Hamilton-Jacobi approaches for systems with purely second class constraints
    (Soc Italiana Fisica, 2003) Baleanu, Dumitru; Güler, Y.
    The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
  • Article
    Multidetermination of thiamine HCl and pyridoxine HCl in their mixture using continuous daubechies and biorthogonal wavelet analysis
    (Elsevier, 2003) Dinç, E.; Baleanu, Dumitru
    A new graphical method based on the one-dimensional wavelet transform (WT) was proposed and tested on mixture of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) in the presence of strongly overlapping signals. We selected from the data of the UV-VIS absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg ml(-1) for each vitamin and we subjected it to Daubechies8 (DAUB8) and Biorthogonal6.8 (BIOR6.8) wavelet transforms. Since the peaks of the transformed signals were bigger than original ones a zero crossing method was applied to obtain the calibration graphs. In addition, the validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. MATLAB 6.5 software was used for one-dimensional wavelet analysis and the basic concepts about wavelet method were given. The obtained results were successfully compared among each other as well as with those obtained by other literature methods. The method developed in this paper is rapid, easy to apply, not expensive and it is suitable for analyzing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment. (C) 2002 Elsevier Science B.V. All rights reserved.
  • Article
    δ-β-Gabor integral operators for a space of locally integrable generalized functions
    (Springer, 2020) Al-Omari, Shrideh Khalaf; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy
    In this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a convolution theorem for the given δ-β-integral. By treating the delta sequences, we derive the necessary axioms to elevate the δ-β-Gabor integrable spaces of Boehmians. The said generalized δ-β-Gabor integral is, therefore, considered as a one-to-one and onto mapping continuous with respect to the usual convergence of the demonstrated spaces. In addition to certain obtained inversion formula, some consistency results are also given.
  • Review
    Variational principles in the frame of certain generalized fractional derivatives
    (Amer Inst Mathematical Sciences-AIMS, 2020) Jarad, Fahd; Abdeljawad, Thabet
    In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.
  • Article
    The first observation of memory effects in the infrared (FT-IR) measurements: Do successive measurements remember each other?
    (Public Library Science, 2014) Nigmatullin, Raoul R.; Osokin, Sergey I.; Baleanu, Dumitru; Al-Amri, Sawsan; Azam, Ameer; Memic, Adnan
    Over the past couple of decades there have been major advances in the field of nanoscience and nanotechnology. Many applications have sprouted from these fields of research. It is essential, given the scale of the materials, to attain accurate, valid and reproducible measurements. Material properties have shown to be a function of their size and composition. Physiochemical properties of the nanomaterials can significantly alter material behavior compared to bulk counterparts. For example, metal oxide nanoparticles have found broad applications ranging from photo-catalysis to antibacterial agents. In our study, we synthesized CuO nanoparticles using well established sol-gel based methods with varying levels of Ni doping. However, upon analysis of measured infrared data, we discovered the presence of quasi-periodic (QP) processes. Such processes have previously been reported to be tightly associated with measurement memory effects. We were able to detect the desired QP process in these measurements from three highly accurate repetitive experiments performed on each Ni (1-7%) doped CuO sample. In other words, successive measurements performed in a rather short period of time remember each other at least inside a group of neighboring measurements.