Matematik Bölümü Yayın Koleksiyonu

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

Browse

Now showing 1 - 20 of 45

Citation - Scopus: 0
A Model to Assist the Maintenance vs. Replacement Decision in Information Systems
(IGI Global, 2013) Pusatli, O.T.; Pusatlı, Özgür Tolga; Regan, B.; 51704; Yönetim Bilişim Sistemleri
An extensive literature review shows that Information Systems (IS) are changed and eventually replaced by substitutes under the influence of productivity, popularity, and specialisation of IS along with associated available support facilities, maintenance activities, failures, and user feedback. This chapter compiles those factors emerged from software engineering, IS, software quality assurance measurements, and computer science literature. A final product is a proposed model bringing those factors together as they are suspected to raise a need for taking the decision of evaluating change requests that may lead to a further maintenance or replace the IS. While keeping in mind that limitations on advanced testing exist, an expected service of such a model may help decision makers to explain maintenance/replacement decision of IS/component in a more itemized manner, hence diminish overburden pressure of experience responsibility on them. © 2014, IGI Global.
Citation - Scopus: 0
A Stability Criterion for Delay Differential Equations With Impulse Effects
(World Scientific Publishing Co., 2007) Alzabut, J.O.; Alzabut, Jehad; Matematik
In this paper, we prove that if a delay differential equation with impulse effects of the form x’(t) = A(t)x(t) + B(t)x(t - τ), t ≠ θi, Δx(θi) = Cix(θi) + Dix(θi-j); i ∈ 2 N; verfies a Perron condition then its trivial solution is uniformly asymptotically stable. © 2007 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.
Citation - Scopus: 6
A Survey on Interpolative and Hybrid Contractions
(Springer, 2021) Karapınar, E.; Karapınar, Erdal; 19184; Matematik
In this chapter, we consider the distinct hybrid type contractions in various abstract spaces. In this work, hybrid contraction refers to combination of not only linear and nonlinear contractions, but also interpolative contractions. The main goal of the chapter is to clarify the metric fixed point theory literature by using the hybrid type contractions that unify several well-known results. © 2021, Springer Nature Switzerland AG.
Citation - Scopus: 8
Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics
(Springer Science and Business Media Deutschland GmbH, 2022) Yang, X.-J.; Baleanu, Dumitru; Baleanu, D.; Srivastava, H.M.; 56389; Matematik
In this chapter, the recent results for the analysis of local fractional calculus are considered for the first time. The local fractional derivative (LFD) and the local fractional integral (LFI) in the fractional (real and complex) sets, the series and transforms involving the Mittag-Leffler function defined on Cantor sets are introduced and reviewed. The uniqueness of the solutions of the local fractional differential and integral equations and the local fractional inequalities are considered in detail. The local fractional vector calculus is applied to describe the Rice theory in fractal fracture mechanics. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 5
Advanced Topics in Fractional Differential Equations A Fixed Point Approach
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
Citation - Scopus: 6
Artificial neural network modeling of systems biology datasets fit based on Mittag-Leffler functions with heavy-tailed distributions for diagnostic and predictive precision medicine
(Elsevier, 2022) Karaca, Y.; Baleanu, Dumitru; Baleanu, D.; 56389; Matematik
Being the most complex physical system in the universe, life, at all scales requires the understanding of the massive complexity including its origin, structure, dynamic, adaptation and organization. Both the number of substructures and interacting pathways of each substructure along with other ones and neurons determine the degree of complexity. Neural networks, as descriptive models, in systems biology setting, provide the means to gather, store and use experiential knowledge; and are designed in a way to emulate different operations of the human brain. One of the major ongoing challenges of integrating fractional calculus in cases of complexity requires an effective use of empirical, numerical, experimental and analytical methods to tackle complexity. In that regard, Artificial Neural Networks (ANNs), including a family of nonlinear computational methods, are employed to handle experimental data in differing domains owing to their capability of tackling complex computations so that their progressive application can solve practical problems. One of the other most noteworthy tools which arises in the fractional calculus context is the Mittag-Leffler (ML) functions. Mittag-Leffler distributions have extensive application domains when dealing with irregular and nonhomogeneous environments for dynamic problems' solutions. They can be used in reliability modeling as an alternative for exponential distribution, particularly this provides upper hand for diagnostic and predictive purposes in precision medicine through novel algorithmic models. To address this, the proposed method in the current study has obtained the generation of optimum model strategies for different biology datasets along with Mittag-Leffler functions with heavy-tailed distributions (see Part I). Within this framework, the proposed integrated approach in this study investigates the dynamics of diseases related to biological elements; and arising in the different solutions of varying complex biological systems, ML function generalizes the exponential function. To this end, firstly, the two-parametric Mittag-Leffler function was applied to biological datasets (cancer cell dataset and diabetes dataset, namely raw datasets), namely cancer cell and diabetes in order to obtain the new datasets (ml_cancer cell dataset and ml_diabetes dataset). Heavy-tailed distributions (The Mittag-Leffler distribution, Pareto distribution, Cauchy distribution and Weibull distribution) were applied to the new datasets obtained with their comparison performed in relation to the performances (by employing the log likelihood value and the Akaike Information Criterion (AIC)). ML functions that represent the cancer cell and diabetes data were identified so that the two parameters Eα,β(z) yielding the optimum value based on the distributions fit could be found. Secondly, one of the ANN algorithms, namely Multi-layer Perceptron (MLP) (along with the accuracy, sensitivity, precision, specificity, F1-score, multi-class classification (MCC), ROC curve), was applied for the diagnosis and prediction of the disease course regarding the optimum ML functions that represent the cancer cell and diabetes datasets obtained and the performances of the ML functions with heavy-tailed distributions were compared with ANN training functions (Levenberg-Marquart, Bayes Regularization and BFGS-Quasi-Newton) accordingly. The integrative modeling scheme proposed herein, which has not been addressed through this sort of approach before, is concerned with the applicability and reliability of the solutions obtained by Mittag-Leffler functions with heavy-tailed distributions. The results obtained by the current study for diseases related to biological datasets based on mathematical models demonstrate that the integrative approach with Mittag-Leffler function and ANN applications is applicable and fits very well to the related data with the robust parameters' values observed and estimated. When the fact that complex biological phenomena involve various intrinsic and extrinsic aspects is considered, it becomes a major difficulty to make identifications and recognition on the basis of a single type of data merely. Thus, the proposed approach of our study corroborates its applicability for diagnostic and predictive purposes in precision medicine through the novel algorithmic model, which plays a significant role in the effective and timely management of unpredictable phenomena in dynamic and nonlinear complex situations. © 2022 Elsevier Inc. All rights reserved.
Citation - Scopus: 8
Computational fractional-order calculus and classical calculus AI for comparative differentiability prediction analyses of complex-systems-grounded paradigm
(Elsevier, 2022) Karaca, Y.; Baleanu, Dumitru; Baleanu, D.; 56389; Matematik
Modern science having embarked on the thorough and accurate interpretation of natural and physical phenomena has proven to provide successful models for the analysis of complex systems and harnessing of control over the various processes therein. Computational complexity, in this regard, comes to the foreground by providing applicable sets of ideas or integrative paradigms to recognize and understand the complex systems' intricate properties. Thus, while making the appropriate, adaptable and evolutive decisions in complex dynamic systems, it is essential to acknowledge different degrees of acceptance of the problems and construct the model it to account for its inherent constraints or limits. In this respect, while hypothesis-driven research has its inherent limitations regarding the investigation of multifactorial and heterogeneous diseases, a data-driven approach enables the examination of the way variables impact one another, which paves the way for the interpretation of dynamic and heterogeneous mechanisms of diseases. Fractional Calculus (FC), in this scope characterized by complexity, provides the applicable means and methods to solve integral, differential and integro-differential equations so FC enables the generalization of integration and differentiation possible in a flexible and consistent manner owing to its capability of reflecting the systems' actual state properties, which exhibit unpredictable variations. The fractional integration and differentiation of fractional-order is capable of providing better characterization of nonstationary and locally self-similar attributes in contrast to constant-order fractional calculus. It becomes possible to model many complex systems by fractional-order derivatives based on fractional calculus so that related syntheses can be realized in a robust and effective way. To this end, our study aims at providing an intermediary facilitating function both for the physicians and individuals by establishing accurate and robust model based on the integration of fractional-order calculus and Artificial Neural Network (ANN) for the diagnostic and differentiability predictive purposes with the diseases which display highly complex properties. The integrative approach we have proposed in this study has a multistage quality the steps of which are stated as follows: first of all, the Caputo fractional-order derivative, one of the fractional-order derivatives, has been used with two-parametric Mittag-Leffler function on the stroke dataset and cancer cell dataset, manifesting biological and neurological attributes. In this way, new fractional models with varying degrees have been established. Mittag-Leffler function, with its distributions of extensive application domains, can address irregular and heterogeneous environments for the solution of dynamic problems; thus, Mittag-Leffler function has been opted for accordingly. Following this application, the new datasets (mlf_stroke dataset and mlf_cancer cell dataset) have been obtained by employing Caputo fractional-order derivative with the two-parametric Mittag-Leffler function (α,β). In addition, classical derivative (calculus) was applied to the raw datasets; and cd_stroke dataset and cd_cancer cell dataset were obtained. Secondly, the performance of the new datasets as obtained from the Caputo fractional derivative with the two-parametric Mittag-Leffler function, the datasets obtained from the classical derivative application and the raw datasets have been compared by using feed forward back propagation (FFBP) algorithm, one of the algorithms of ANN (along with accuracy rate, sensitivity, precision, specificity, F1-score, multiclass classification (MCC), ROC curve). Based on the accuracy rate results obtained from the application with FFBP, the Caputo fractional-order derivative model that is most suitable for the diseases has been generated. The experimental results obtained demonstrate the applicability of the complex-systems-grounded paradigm scheme as proposed through this study, which has no existing counterpart. The integrative multi-stage method based on mathematical-informed framework with comparative differentiability prediction analyses can point toward a new direction in the various areas of applied sciences to address formidable challenges of critical decision making and management of chaotic processes in different complex dynamic systems. © 2022 Elsevier Inc. All rights reserved.
Citation - WoS: 0
Coordinate systems of Cantor-type cylindrical and Cantor-type spherical coordinates
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - Scopus: 4
Coupled Systems for Fractional Differential Equations
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
This chapter deals with some existence and uniqueness results for a class of coupled systems for nonlinear k-generalized ψ -Hilfer fractional differential equations with boundary and terminal conditions. Our results are based on some necessary fixed point theorems. Furthermore, an illustration is presented for each section to demonstrate the plausibility of our results. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - WoS: 0
Coupling the local fractional Laplace transform with analytic methods
(Academic Press Ltd-elsevier Science Ltd, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Srivastava, H. M.; 56389; Matematik
Citation - Scopus: 1
Cyber Attacks and Preliminary Steps in Cyber Security in National Protection
(IGI Global, 2018) Aydin, F.; Pusatlı, Özgür Tolga; Tolga Pusatli, O.; 51704; Yönetim Bilişim Sistemleri
Cyber attacks launched by individuals and/or supported by nation states have increased due to the prevalence of information technologies at critical infrastructure of the states. In this chapter, such attacks and consecutive impacts are visited. In connection with this issue, evolution of cyber threats from annoying malware to serious weapons is studied by examples; hence, precautions against such threats are visited and usage of anti-malware applications as prevalent precautions is assessed within the scope. Selected information security standards and strategies of selected states and precautions for cyber security of Turkey are studied. Our findings underline that educated citizens and companies along with public institutions should cooperate to provide a nationwide cyber security. Consequently, it is defended that governments should play an affective role to protect, educate, and guide governmental and private companies and citizens on the cyber security by promoting the cyber security topic in the successive national development plans. © 2018 by IGI Global. All rights reserved.
Citation - WoS: 7
Delay Effects on the Dynamics of the Lengyel-Epstein Reaction-Diffusion Model
(Springer international Publishing Ag, 2016) Merdan, Huseyin; Bilazeroğlu, Şeyma; Kayan, Seyma; 49206; Matematik
Citation - Scopus: 13
Discrete fractional masks and their applications to image enhancement
(De Gruyter, 2019) Wu, G.-C.; Baleanu, Dumitru; Baleanu, D.; Bai, Y.-R.; 56389; Matematik
Fractional differences for image enhancement are revisited and the general methodology is illustrated in this chapter. Several fractional differences are theoretically analyzed and numerically compared. The weight coefficients derived from the discrete fractional calculus are a set of conserved quantities and they are suitable for image processing. Then a discrete fractional mask is designed within the Caputo difference and the mask coefficients are given by use of the Gamma functions. In comparison with the Grünwald-Letnikov difference and Riemann-Liouville masks, the results show this novel mask’s efficiency and simplicity. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
Citation - Scopus: 4
Fractional analogous models in mechanics and gravity theories
(Springer New York, 2012) Baleanu, D.; Baleanu, Dumitru; Vacaru, S.I.; 56389; Matematik
Each chapter should be preceded by an abstract (10-15 lines long) that summarizes the content. The abstract will appear online at www.SpringerLink.com and be available with unrestricted access. This allows unregistered users to read the abstract as a teaser for the complete chapter. As a general rule the abstracts will not appear in the printed version of your book unless it is the style of your particular book or that of the series to which your book belongs. Please use the ‘starred’ version of the new Springer abstract command for typesetting the text of the online abstracts (cf. source file of this chapter template abstract) and include them with the source files of your manuscript. Use the plain abstract command if the abstract is also to appear in the printed version of the book. © Springer Science+Business Media, LLC 2012. All rights reserved.
Citation - Scopus: 10
Fractional calculus for modeling unconfined groundwater
(De Gruyter, 2019) Jafari, H.; Baleanu, Dumitru; Mehdinejadiani, B.; Baleanu, D.; 56389; Matematik
The porous medium which groundwater flows in is heterogeneous at all scales. This complicates the simulation of groundwater flow. Fractional derivatives, because of their non-locality property, can reduce the scale effects on the parameters and, consequently, better simulate the hydrogeological processes. In this chapter a fractional governing partial differential equation on unconfined groundwater (fractional Boussinesq equation [FBE]) is derived using the fractional mass conservation law. The FBE is a generalization of the Boussinesq equation (BE) that can be used in both homogeneous and heterogeneous unconfined aquifers. Compared to the BE, the FBE includes an additional parameter which represents the heterogeneity degree of the porous medium. This parameter changes within the range of 0 to 1 in the non-linear form of the FBE. The smaller the value of the heterogeneity degree, the more heterogeneous the aquifer is, and vice versa. To investigate the applicability of the FBE to real problems in groundwater flow, a fractional Glover-Dumm equation (FGDE) was obtained using an analytical solution of the linear form of the FBE for onedimensional unsteady flow towards parallel subsurface drains. The FGDE was fitted to water table profiles observed at laboratory and field scales, and its performance was compared to that of the Glover-Dumm equation (GDE). The parameters of the FGDE and the GDE were estimated using the inverse problem method. The results indicate that one can recognize the heterogeneity degree of porous media examined according to the obtained values for the indicator of the heterogeneity degree. The FGDE and the GDE showed similar performances in homogeneous soil, while the performance of the FGDE was significantly better than that of the GDE in heterogeneous soil. In summary, the FBE can be used as a highly general differential equation governing groundwater flow in unconfined aquifers. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
Citation - Scopus: 10
Fractional differential equations with bio-medical applications
(De Gruyter, 2019) Arshad, S.; Baleanu, Dumitru; Baleanu, D.; Tang, Y.; 56389; Matematik
In this chapter, we investigate the dynamics of fractional order models in bio-medical. First, we examine the fractional order model of HIV Infection and analyze the stability results for non-infected and infected equilibrium points. Then, we concentrate on the fractional order tumor growth model and establish a sufficient condition for existence and uniqueness of the solution of the fractional order tumor growth model. Local stability of the four equilibrium points of the model, namely the tumor free equilibrium, the dead equilibrium of type 1, the dead equilibrium of type 2 and the coexisting equilibrium is investigated by applying Matignons condition. Dynamics of the fractional order tumor model is numerically investigated by varying the fractional-order parameter and the system parameters. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
Citation - Scopus: 6
Fractional Differential Equations with Instantaneous Impulses
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
The aim of this chapter is to prove some existence, uniqueness, and Ulam-Hyers-Rassias stability results for a class of boundary value problem for nonlinear implicit fractional differential equations with impulses and generalized Hilfer-type fractional derivative. We base our arguments on some relevant fixed point theorems combined with the technique of measure of noncompactness. Examples are included to show the applicability of our results for each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 3
Fractional Differential Equations with Non-Instantaneous Impulses
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
The present chapter deals with some existence, uniqueness, and Ulam stability results for a class of initial and boundary value problems for nonlinear implicit fractional differential equations with non-instantaneous impulses and generalized Hilfer-type fractional derivative. The tools employed are some suitable fixed point theorems combined with the technique of measure of noncompactness. We provide illustrations to demonstrate the applicability of our results for each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 4
Fractional Differential Equations with Retardation and Anticipation
(Springer Nature, 2023) Benchohra, M.; Karapınar, Erdal; Karapınar, E.; Lazreg, J.E.; Salim, A.; 19184; Matematik
In this chapter, we prove some existence and uniqueness results for a class of boundary and terminal value problems for implicit nonlinear k-generalized ψ -Hilfer fractional differential equations involving both retarded and advanced arguments. Further, examples are given to illustrate the viability of our results in each section. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Citation - Scopus: 2
Fractional Exact Solutions and Solitons in Gravity
(Springer New York, 2012) Baleanu, D.; Baleanu, Dumitru; Vacaru, S.I.; 56389; Matematik
Each chapter should be preceded by an abstract (10-15 lines long) that summarizes the content. The abstract will appear online at www.?SpringerLink.?com and be available with unrestricted access. This allows unregistered users to read the abstract as a teaser for the complete chapter. As a general rule the abstracts will not appear in the printed version of your book unless it is the style of your particular book or that of the series to which your book belongs. Please use the ’starred’ version of the new Springer abstract command for typesetting the text of the online abstracts (cf. source file of this chapter template abstract) and include them with the source files of your manuscript. Use the plain abstract command if the abstract is also to appear in the printed version of the book. © Springer Science+Business Media, LLC 2012. All rights reserved.

Browse

Browsing Matematik Bölümü Yayın Koleksiyonu by Publication Category "Kitap Bölümü - Uluslararası"