Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Baleanu, DumitruPublisher: search.filters.publisher.Springer international Publishing Ag

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  • Conference Object
    Citation - Scopus: 1
    Fractional Order Computing and Modeling With Portending Complex Fit Real-World Data
    (Springer international Publishing Ag, 2023) Rahman, Mati Ur; Baleanu, Dumitru; Karaca, Yeliz
    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.
  • Conference Object
    Citation - WoS: 1
    Citation - Scopus: 3
    Theory, Analyses and Predictions of Multifractal Formalism and Multifractal Modelling for Stroke Subtypes' Classification
    (Springer international Publishing Ag, 2020) Baleanu, Dumitru; Moonis, Majaz; Zhang, Yu-Dong; Karaca, Yeliz
    Fractal and multifractal analysis interplay within complementary methodology is of pivotal importance in ubiquitously natural and man-made systems. Since the brain as a complex system operates on multitude of scales, the characterization of its dynamics through detection of self-similarity and regularity presents certain challenges. One framework to dig into complex dynamics and structure is to use intricate properties of multifractals. Morphological and functional points of view guide the analysis of the central nervous system (CNS). The former focuses on the fractal and self-similar geometry at various levels of analysis ranging from one single cell to complicated networks of cells. The latter point of view is defined by a hierarchical organization where self-similar elements are embedded within one another. Stroke is a CNS disorder that occurs via a complex network of vessels and arteries. Considering this profound complexity, the principal aim of this study is to develop a complementary methodology to enable the detection of subtle details concerning stroke which may easily be overlooked during the regular treatment procedures. In the proposed method of our study, multifractal regularization method has been employed for singularity analysis to extract the hidden patterns in stroke dataset with two different approaches. As the first approach, decision tree, Naive bayes, kNN and MLP algorithms were applied to the stroke dataset. The second approach is made up of two stages: i) multifractal regularization (kulback normalization) method was applied to the stroke dataset and mFr stroke dataset was generated. ii) the four algorithms stated above were applied to the mFr stroke dataset. When we compared the experimental results obtained from the stroke dataset and mFr stroke dataset based on accuracy (specificity, sensitivity, precision, F1-score and Matthews Correlation Coefficient), it was revealed that mFr stroke dataset achieved higher accuracy rates. Our novel proposed approach can serve for the understanding and taking under control the transient features of stroke. Notably, the study has revealed the reliability, applicability and high accuracy via the methods proposed. Thus, the integrated method has revealed the significance of fractal patterns and accurate prediction of diseases in diagnostic and other critical-decision making processes in related fields.
  • Conference Object
    Citation - Scopus: 2
    Multifractional Gaussian Process Based on Self-Similarity Modelling for Ms Subgroups' Clustering With Fuzzy C-Means
    (Springer international Publishing Ag, 2020) Baleanu, Dumitru; Karaca, Yeliz
    Multifractal analysis is a beneficial way to systematically characterize the heterogeneous nature of both theoretical and experimental patterns of fractal. Multifractal analysis tackles the singularity structure of functions or signals locally and globally. While Holder exponent at each point provides the local information, the global information is attained by characterization of the statistical or geometrical distribution of Holder exponents occurring, referred to as multifractal spectrum. This analysis is time-saving while dealing with irregular signals; hence, such analysis is used extensively. Multiple Sclerosis (MS), is an auto-immune disease that is chronic and characterized by the damage to the Central Nervous System (CNS), is a neurological disorder exhibiting dissimilar and irregular attributes varying among patients. In our study, the MS dataset consists of the Expanded Disability Status Scale (EDSS) scores and Magnetic Resonance Imaging (MRI) (taken in different years) of patients diagnosed with MS subgroups (relapsing remitting MS (RRMS), secondary progressive MS (SPMS) and primary progressive MS (PPMS)) while healthy individuals constitute the control group. This study aims to identify similar attributes in homogeneous MS clusters and dissimilar attributes in different MS subgroup clusters. Thus, it has been aimed to demonstrate the applicability and accuracy of the proposed method based on such cluster formation. Within this framework, the approach we propose follows these steps for the classification of the MS dataset. Firstly, Multifractal denoising with Gaussian process is employed for identifying the critical and significant self-similar attributes through the removal of MS dataset noise, by which, mFd MS dataset is generated. As another step, Fuzzy C-means algorithm is applied to the MS dataset for the classification purposes of both datasets. Based on the experimental results derived within the scheme of the applicable and efficient proposed method, it is shown that mFd MS dataset yielded a higher accuracy rate since the critical and significant self-similar attributes were identified in the process. This study can provide future direction in different fields such as medicine, natural sciences and engineering as a result of the model proposed and the application of alternative mathematical models. As obtained based on the model, the experimental results of the study confirm the efficiency, reliability and applicability of the proposed method. Thus, it is hoped that the derived results based on the thorough analyses and algorithmic applications will be assisting in terms of guidance for the related studies in the future.
  • Article
    Citation - WoS: 58
    Citation - Scopus: 64
    On Two Fractional Differential Inclusions
    (Springer international Publishing Ag, 2016) Hedayati, Vahid; Rezapour, Shahram; Al Qurashi, Maysaa' Mohamed; Baleanu, Dumitru
    We investigate in this manuscript the existence of solution for two fractional differential inclusions. At first we discuss the existence of solution of a class of fractional hybrid differential inclusions. To illustrate our results we present an illustrative example. We study the existence and dimension of the solution set for some fractional differential inclusions.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 15
    A Novel Computational Approach To Approximate Fuzzy Interpolation Polynomials
    (Springer international Publishing Ag, 2016) Jafari, Raheleh; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; Jafarian, Ahmad; Mohamed Al Qurashi, Maysaa
    This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form y(p) = a(n)x(p)(n) +... + a(1)x(p) + a(0) where a(j) is crisp number (for j = 0,..., n), which interpolates the fuzzy data (x(j), y(j)) (for j = 0,..., n). Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient.
  • Article
    Citation - WoS: 25
    Citation - Scopus: 29
    A New Approach for One-Dimensional Sine-Gordon Equation
    (Springer international Publishing Ag, 2016) Inc, Mustafa; Kilicman, Adem; Baleanu, Dumitru; Akgul, Ali
    In this work, we use a reproducing kernel method for investigating the sine-Gordon equation with initial and boundary conditions. Numerical experiments are studied to show the efficiency of the technique. The acquired results are compared with the exact solutions and results obtained by different methods. These results indicate that the reproducing kernel method is very effective.
  • Article
    Citation - WoS: 23
    Citation - Scopus: 26
    Numerical Solution of Linear Integral Equations System Using the Bernstein Collocation Method
    (Springer international Publishing Ag, 2013) Nia, Safa A. Measoomy; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Jafarian, Ahmad
    Since in some application mathematical problems finding the analytical solution is too complicated, in recent years a lot of attention has been devoted by researchers to find the numerical solution of this equations. In this paper, an application of the Bernstein polynomials expansion method is applied to solve linear second kind Fredholm and Volterra integral equations systems. This work reduces the integral equations system to a linear system in generalized case such that the solution of the resulting system yields the unknown Bernstein coefficients of the solutions. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.
  • Article
    Citation - WoS: 52
    Citation - Scopus: 57
    Damped Wave Equation and Dissipative Wave Equation in Fractal Strings Within the Local Fractional Variational Iteration Method
    (Springer international Publishing Ag, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Jafari, Hossein; Su, Wei-Hua
    In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the methodology of local fractional variational iteration method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions. MSC: 74H10, 35L05, 28A80.
  • Article
    Citation - WoS: 52
    Citation - Scopus: 57
    On a Nonlinear Fractional Differential Equation on Partially Ordered Metric Spaces
    (Springer international Publishing Ag, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
    In this paper, by using a fixed point result on ordered metric spaces, we prove the existence and uniqueness of a solution of the nonlinear fractional differential equation (, ) via the periodic boundary condition , where and is a continuous increasing function and denotes the Caputo fractional derivative of order alpha. Also, we solve it by using the anti-periodic boundary conditions with and with and separately.
  • Article
    Citation - WoS: 96
    Citation - Scopus: 117
    A Jacobi Operational Matrix for Solving a Fuzzy Linear Fractional Differential Equation
    (Springer international Publishing Ag, 2013) Suleiman, Mohamed; Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, Ali
    This paper reveals a computational method based using a tau method with Jacobi polynomials for the solution of fuzzy linear fractional differential equations of order . A suitable representation of the fuzzy solution via Jacobi polynomials diminishes its numerical results to the solution of a system of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The efficiency and applicability of the proposed method are proved by several test examples.