Yeliz Karaca

University of Massachusetts Chan Medical School

Neural networks and fractional order calculus are powerful tools for system identification through which there exists the capability of approximating nonlinear functions owing to the use of nonlinear activation functions and of processing diverse inputs and outputs as well as the automatic adaptation of synaptic elements through a specified learnin...

Deterministic and fractional properties of an epidemic model for the dynamics of the Middle Eastern respiratory syndrome coronavirus (MERS-COV) with various infection stages are pro-posed in the current study whose aim is to show via a mathematical model the transmission of MERS-COV between humans and camels, which are suspected to be the primary s...

Power series, as an important means to analyze functions in different complex settings, are employed in various applied areas to solve differential equations and nonlinear problems and provide the assessment of intervals of convergence. Accordingly, the fuzzy logistic differential equation using the Caputo operator has been studied in this paper. T...

In this paper, we present new existence results for the quasi-variational inequality problem (QV I) in reflexive Banach spaces using the fixed point method with quasi-monotonicity and local upper sign-continuity assumptions. These results improve upon previous ones which only required a weaker monotonicity condition and did not impose compactness o...

https://dergipark.org.tr/en/pub/chaos/issue/73767

The non-instantaneous condition is utilized in our study through the employment of the Cauchy problem in order to contract a system of nonlinear non-autonomous mixed-type integro-differential (ID) fractional evolution equations in infinite-dimensional Banach spaces. We reveal the existence of new mild solutions in the condition that the nonlinear f...

In this paper, we aim to discuss a fractional complex Ginzburg–Landau equation by using the parabolic law and the law of weak non-local nonlinearity. Then, we derive dynamic behaviors of the given model under certain parameter regions by employing the planar dynamical system theory. Further, we apply the ansatz method to derive soliton, bright and...

Complex problems in nonlinear dynamics foreground the critical support of artificial phenomena so that each domain of complex systems can generate applicable answers and solutions to the pressing challenges. This sort of view is capable of serving the needs of different aspects of complexity by minimizing the problems of complexity whose solutions...

https://dergipark.org.tr/en/pub/chaos/issue/73033

Incorporating self-diffusion and super-cross diffusion factors into the modeling approach enhances efficiency and realism by having a substantial impact on the scenario of pattern formation. Accordingly, this work analyzes self and super-cross diffusion for a predator-prey model. First, the stability of equilibrium points is explored. Utilizing sta...

Fractional calculus approach, providing novel models through the introduction of fractional-order calculus to optimization methods, is employed in machine learning algorithms. This scheme aims to attain optimized solutions by maximizing the accuracy of the model and minimizing the functions like the computational burden. Mathematical-informed frame...

Nonlinear functional-integral equations contain the unknown function nonlinearly, occurring extensively in theory developed to a certain extent toward different applied problems and solutions thereof. Nonlinear science serves to reveal the nonlinear descriptions of widely different systems, has had a fundamental impact on complex dynamics. Accordin...

The aim of this paper is to investigate the approximate solutions of nonlinear temporal fractional models of Gardner and Cahn-Hillard equations. The fractional models of the Gardner and Cahn-Hilliard equations play an important role in pulse propagation in dispersive media. The time-fractional derivative is observed in the conformable framework. In...

This paper presents a theoretical and complex numerical analysis of the 2-torus chaotic system with a power-law kernel. Various dynamical characteristics of the complex system are investigated covering existence uniqueness, attractor projection, time series analysis and sensitivity towards initial values. 4-torus attractor coexistence is observed w...

Fractals, as a universal language, are often considered to be an abundant source of creativity, surprise, beauty and reality. Being regarded and employed as a powerful tool to communicate, interpret, describe and analyze complex ideas and complexity in nature and other imaginable systems, fractals can most of the time remind one of a story or a nar...

Consumption of renewable energy is on the rise because new technologies have made it cheaper and easier to meet the needs of a long-term energy source. In the present study, the idea of optimal usage of sustainable energy is discussed, taking into consideration the environmental and economic conditions that exist in Pakistan's textile manufacturing...

Advanced Fractals and Fractional Calculus with Science and Engineering Applications: Computing, Dynamics and Control in Complex Systems

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, c...

Fractals, being essentially mathematical constructs, are forms that embody the fundamental features of dynamism, self-organization, self-similarity and complexity. The lexical items and parts of sentences are comprehended as the constituents of schemata with a particular pattern made up of interacting elements. Among the most well-known means used...

Having existed as a term since antiquity complexity as an idea and scientific concept that requires the understanding of origin of complex components entails lengthy and meticulous computations, as well as causal processes. A complex system, in that regard, is literally one where multiple interactions occur and emerge among the components; and comm...

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...

Complex dynamic characteristics of systems based on entropy entail a detailed specification and synthesis of the intricate elements, as the system gets more and more complex. The growth of complexity, in more nonlinear and complicated instances, evolves with increasing information and entropy in a monotonous way. Multilevel analyses are to be emplo...

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. N...

Differential equations with complex order fractional derivatives enable the regulation of complicated fractional systems. Within this scale, fractional calculus unfolds the fundamental mechanisms and multi-scale dynamic phenomena in biological tissues. It is viable that weakly nonlinear analysis represents a system that includes amplitude equations...

Modern scientific thinking adopts the systemic properties and addresses them through revealing the spontaneous processes related to self-organization in a dynamical system in a state far from the equilibrium point and close to the disequilibrium point with no existence of external force acting upon the system. The modern way of thinking poses a cha...

Complexity of living organisms owing to their inherent functional properties points toward a systems biology approach due to the fact that structural and topological uncertainties exist along with abrupt transitions characterized by unknown inputs, time-varying parameters and unpredictable observation states. The related uncertain, emergent and evo...

Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems is an edited book that addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, n...

Fuzzy mathematics-informed methods are bene cial in cases when observations display uncertainty and volatility since it is of vital importance to make predictions about the future considering the stages of interpreting, planning, and strategy building. It is possible to realize this aim through accurate, reliable, and realistic data and information...

Since ecological systems are history-dependent, incorporating fractional calculus and especially variable order ones could significantly improve the emulation of these systems. Nonetheless, in the literature, no study considers ecological processes by variable-order fractional (VOF) model. This study is motivated by this issue. At first, we propose...

In this study, we model the fractal-fractional system of the Computer virus problem using the Atangana–Baleanu operator. Moreover, we have presented the existence and the uniqueness of the results under applying the Schauder fixed point and Banach fixed theorems. We have used the Atangana–Toufik technique to obtain the approximate solutions by choo...

This paper introduces some important dissipative problems that are recent and still of intermittent interest. The classical dynamics of Helmholtz and Kelvin–Helmholtz instability equations are modeled with the Riesz operator which incorporates the left- and right-sided of the Riemann–Liouville non-integer order operators to mimic naturally the phys...

Hidden Markov Model (HMM) is a stochastic process where implicit or latent stochastic processes can be inferred indirectly through a sequence of observed states. HMM as a mathematical model for uncertain phenomena is applicable for the description and computation of complex dynamical behaviours enabling the mathematical formulation of neural dynami...

In the ever-evolving vibrant landscape of our times, it is crucial that a peaceful environment is ensured taking into account all the likely ecological parameters along with humidity and temperature while conserving energy. us, besides mechanical and electric control systems, it has become vital to ensure that arti cial intelligence (AI) is assimil...

In today’s sophisticated global marketplace, supply chains are complex nonlinear systems in the presence of different types of uncertainties, including supply-demand and delivery uncertainties. Though up to now, some features of these systems are studied, there are still many aspects of these systems which need more attention. This necessitates mor...

Mathematical modeling can be utilized to find out how the coronavirus spreads within a population. Hence, considering models that can precisely describe natural phenomena is of crucial necessity. Besides, although one of the most significant benefits of mathematical modeling is designing optimal policies for battling the disease, there are a few st...

In this paper, some new fractal versions of Fejér–Hermite–Hadamard (FHH) type variants for generalized Raina [Formula: see text]-convex mappings are established benefiting from Raina’s function and fractal set [Formula: see text]. By means of three integral identities coupled with Raina’s function and local differentiation, we established some boun...

In this study, a synchronization problem for spatio-temporal partial differential systems is addressed and researched within a subjectivist framework. In light of Lyapunov direct method and some proposed nonlinear controllers, a new scheme is established to accomplish a full synchronization between two reaction–diffusion systems of integer- and fra...

The purpose of this paper is to explore novel variants for convex functions via discrete [Formula: see text]-fractional operator in the frame of time scale calculus [Formula: see text] with [Formula: see text] and [Formula: see text] Based on a comparison with the integral inequalities, we have provided new discrete fractional inequalities having [...

New fractional operators have the aim of attracting nonlocal problems that display fractal behaviour; and thus fractional derivatives have applications in long-term relation description along with micro-scaled and macro-scaled phenomena. Formulated by fractional operators, the formulation of a dynamical system is used in applications for the descri...

Aim: Tuberculosis is an infectious disease caused by Mycobacterium tuberculosis bacteria. This study plans to build a novel deep learning-based model for the accurate recognition of tuberculosis. Methods: We propose a novel model — rotation angle vector grid-based fractional Fourier entropy and deep stacked sparse autoencoder (RAVG-FrFE–DSSAE) — wh...

The universe, with its fractal structure patterns, includes infinite array of elements interacting in complex systems, while manifesting adaptability, self-organization and sensitivity to the external environment. A fractal system is also a nonlinear, complex and interactive system capable of adapting to a vague environment where Fractional Calculu...

This study contributes to the major consequences of the certain novel versions of reverse Minkowski and related Holder type inequalities via discrete h-proportional fractional sums are presented. The proposed system has an intriguing feature not investigated in the literature so far, it is characterized by the nabla h-fractional sums. Novel special...

A weakly nonlinear analysis provides a system constituting amplitude equations and its related analysis is capable of predicting parameter regimes with different patterns is expected to co-exist in dynamical circumstances that exhibit complex fractional-order system characteristics. The Turing mechanism of pattern formation as a result of diffusion...

In the version of this paper 27 was originally published the name of Marcela Velásquez Fernádez has been corrected to Marrcela Velásquez Fernández. In the version of this paper 44 was originally published the name of Łukasz Tomczyk – at appears with a “v” at the end of this family name. This has now been corrected.

The purpose of this paper is to provide novel estimates of Ostrowski-type inequalities in a much simpler and shorter way of some recent significant results in the context of a fractal set [Formula: see text] By using our new approach, we established an auxiliary result that correlates with generalized convex ([Formula: see text]) and concave functi...

This work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized [Formula: see text]-convex and approximately [Formula: see text]-quasiconvex function, with respect to Raina’s function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed...

A user-friendly approach depending on nonlocal kernel has been constituted in this study to model nonlocal behaviors of fractional differential and difference equations, which is known as a generalized proportional fractional operator in the Hilfer sense. It is deemed, for differentiable functions, by a fractional integral operator applied to the d...

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 t...

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 Hölder exponent at each point provides the local information, the global information i...

The seven volumes LNCS 12249-12255 constitute the refereed proceedings of the 20th International Conference on Computational Science and Its Applications, ICCSA 2020, held in Cagliari, Italy, in July 2020. Due to COVID-19 pandemic the conference was organized in an online event. Computational Science is the main pillar of most of the present resear...

Glomerulosclerosis is a pathomorphological feature of glomerular lesions. Early detection, accurate judgement and effective prevention of the glomeruli is crucial not only for people with kidney disease, but also for the general population. We proposed a method in combination of traditional image analysis with modern machine learning diagnosis syst...

The seven volumes LNCS 12249-12255 constitute the refereed proceedings of the 20th International Conference on Computational Science and Its Applications, ICCSA 2020, held in Cagliari, Italy, in July 2020. Due to COVID-19 pandemic the conference was organized in an online event. Computational Science is the main pillar of most of the present resear...

The seven volumes LNCS 12249-12255 constitute the refereed proceedings of the 20th International Conference on Computational Science and Its Applications, ICCSA 2020, held in Cagliari, Italy, in July 2020. Due to COVID-19 pandemic the conference was organized in an online event. Computational Science is the main pillar of most of the present resear...

The seven volumes LNCS 12249-12255 constitute the refereed proceedings of the 20th International Conference on Computational Science and Its Applications, ICCSA 2020, held in Cagliari, Italy, in July 2020. Due to COVID-19 pandemic the conference was organized in an online event. Computational Science is the main pillar of most of the present resear...

The seven volumes LNCS 12249-12255 constitute the refereed proceedings of the 20th International Conference on Computational Science and Its Applications, ICCSA 2020, held in Cagliari, Italy, in July 2020. Due to COVID-19 pandemic the conference was organized in an online event. Computational Science is the main pillar of most of the present resear...

This paper addresses the concept of an up-to-date transdisciplinary system modelling based on decision tree within the framework of systems theory. Systems theory constructs effective models for the analysis of complex systems since this comprehensive theory is capable of providing links between the problems and dynamics of systems. Particularly, f...

Numerous natural phenomena display repeating self-similar patterns. Fractal is used when a pattern seems to repeat itself. Fractal and multifractal methods have extensive applications in neurosciences in which the prevalence of fractal properties like self-similarity in the brain, equipped with a complex structure, in medical data analysis at vario...

It has become vital to effectively characterize the self-similar and regular patterns in time series marked by short-term and long-term memory in various fields in the ever-changing and complex global landscape. Within this framework, attempting to find solutions with adaptive mathematical models emerges as a major endeavor in economics whose compl...

Complex systems constitute components that interact with one another and involve phenomena which are not always easy to understand in terms of their components and interactions. Alternative mathematical models have been developed so that the users’ tasks can be facilitated and an actual assistance can be provided for decision-making processes in ca...

The seven volumes LNCS 12249-12255 constitute the refereed proceedings of the 20th International Conference on Computational Science and Its Applications, ICCSA 2020, held in Cagliari, Italy, in July 2020. Due to COVID-19 pandemic the conference was organized in an online event. Computational Science is the main pillar of most of the present resear...

Fractal and multifractal geometries have been applied extensively in various medical signals which exhibit fractal characteristics. Application of such geometries rests on the estimation of fractal features. Within this framework, various methods have been proposed for the estimation of the multifractal spectral or fractal dimension of a particular...

Multifractal methods are employed to recognize the significant attributes through the removal of the noise in any dataset. Being a useful and sensitive technological tool, magnetic resonance imaging (MRI) is employed for the diagnosis of chronic diseases of the central nervous system, one of which is Multiple Sclerosis disease (MS). MS subgroups (P...

This study is concerned with local Hölder exponent as a function regularity measure for time series regarding Finance data. The study examines 12 attributes in the Micro, Small and Medium Enterprises (MSME) data for 6 regions (2004–2018). The study has two different approaches. Firstly, (i) multi fractal methods and Brownian motion Hölder regularit...

Support vector machine (SVM) is one of the most frequently used algorithms utilized for classification. When a classification rule is constructed through the SVM, it is of fundamental importance to evaluate its prediction accuracy. In this study, the kernel types of SVM kernels were applied on to the dataset whose attributes were based on the Wechs...

Information technology has recently seen a huge progress in innovative healthcare technologies that rendered healthcare data bigger. Connectivity on 7/24 basis between human to device and device to device have a crucial role in individuals’ lives. Therefore, Mobile Cloud System (MCC) has become an indispensable tool. Parallel with the rapid develop...

This comprehensive book provides the readers with the core skills regarding data analysis and the application of algorithms. The book helps the readers establish a transition from equations to the source codes related to algorithms and from the interpretation of results to draw meaningful information about data within the real dataset and synthetic...

In Diffusion Limited Aggregation (DLA), the procedure in which substances blend irrevocably to produce dendrites, is idealised. During this process, the slowest phase tends to be the diffusion of substance to aggregate. This study focuses on the procedure where substances enduring a random walk because of Brownian motion cluster together to form ag...

Magnetic Resonance Image segmentation is the process of partitioning brain data, which is regarded as a highly challenging task for medical applications, particularly in Alzheimer’s Disease (AD). In this study, we have developed a new automatic segmentation algorithm which can be seen as a novel decision making technique that can help diagnose deci...

Feature extraction is a kind of dimensionality reduction which refers to the differentiating features of a dataset. In this study, we have worked on ESD_Data Set (33 attributes), composed of clinical and histopathological attributes of erythematous-squamous skin diseases (ESDs) (psoriasis, seborrheic dermatitis, lichen planus, pityriasis rosea, chr...

Multifractal denoising techniques capture interest in biomedicine, economy, and signal and image processing. Regarding stroke data there are subtle details not easily detectable by eye physicians. For the stroke subtypes diagnosis, details are important due to including hidden information concerning the possible existence of medical history, labora...

In this study, 1 D wavelet and Partial correlation analyses were applied to a data set obtained from patients with Multiple Sclerosis along with a control group of healthy individuals. The analysis is limited to a sample of 139 individuals, 76 being with Relapsing-Remitting Multiple Sclerosis, 38 with Secondary Progressive Multiple Sclerosis, 6 wit...

Machine learning methods are frequently used for data sets in many fields including medicine for purposes of feature extraction and pattern recognition. This study includes lesion data obtained from Magnetic Resonance images taken in three different years and belonging to 120 individuals (with 76 RRMS, 6 PPMS, 38 SPMS). Many alternative methods are...

The development of globalization means that economies of the world are placing more importance on international trade. The increase in the variety of goods or services and the implementation of deregulation policies by many countries have made increases in international trade unavoidable. This study investigates the relationship between Turkey’s in...

Magnetic resonance imaging (MRI) is the most sensitive method to detect chronic nervous system diseases such as multiple sclerosis (MS). In this paper, Brownian motion Hölder regularity functions (polynomial, periodic (sine), exponential) for 2D image, such as multifractal methods were applied to MR brain images, aiming to easily identify distresse...

Our purpose is to develop a clinical decision support system to classify the patients' diagnostics based on features gathered from Magnetic Resonance Imaging (MRI) and Expanded Disability Status Scale (EDSS). We studied 120 patients and 19 healthy individuals (not afflicted with MS) have been studied for this study. Healthy individuals in the contr...

The main aim of this paper is to classify mental functions by the Wechsler Adult Intelligence Scale-Revised tests with a mixed method based on wavelets and partial correlation. The Wechsler Adult Intelligence Scale-Revised is a widely used test designed and applied for the classification of the adults cognitive skills in a comprehensive manner. In...