Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
5 results
Search Results
Article Citation - WoS: 14Citation - Scopus: 15New Multi-Functional Approach for Κth-Order Differentiability Governed by Fractional Calculus Via Approximately Generalized (Ψ, (h)over-Bar) Functions in Hilbert Space(World Scientific Publ Co Pte Ltd, 2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-MingThis work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex and approximately psi-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions such as higher-order strongly (HOS) generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions and HOS generalized psi-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized psi-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields.Editorial Citation - WoS: 1Citation - Scopus: 2Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part Iii(World Scientific Publ Co Pte Ltd, 2022) Baleanu, Dumitru; Moonis, Majaz; Zhang, Yu-Dong; Gervasi, Osvaldo; Karaca, YelizEditorial Citation - WoS: 4Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part I(World Scientific Publ Co Pte Ltd, 2021) Baleanu, Dumitru; Moonis, Majaz; Muhammad, Khan; Zhang, Yu-Dong; Gervasi, Osvaldo; Karaca, YelizArticle Citation - WoS: 17Citation - Scopus: 19Achieving More Precise Bounds Based on Double and Triple Integral as Proposed by Generalized Proportional Fractional Operators in the Hilfer Sense(World Scientific Publ Co Pte Ltd, 2021) Rashid, Saima; Karaca, Yeliz; Hammouch, Zakia; Baleanu, Dumitru; Chu, Yu-Ming; Al-Qurashi, MaysaaA 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 derivative of a function having an exponential function in the kernel. This operator generalizes a novel version of Cebysev-type inequality in two and three variables sense and furthers the result of existing literature as a particular case of the Cebysev inequality is discussed. Some novel special cases are also apprehended and compared with existing results. The outcome obtained by this study is very broad in nature and fits in terms of yielding an enormous number of relating results simply by practicing the proportionality indices included therein. Furthermore, the outcome of our study demonstrates that the proposed plans are of significant importance and computationally appealing to deal with comparable sorts of differential equations. Taken together, the results can serve as efficient and robust means for the purpose of investigating specific classes of integrodifferential equations.Article Citation - WoS: 33Citation - Scopus: 40A Novel R/S Fractal Analysis and Wavelet Entropy Characterization Approach for Robust Forecasting Based on Self-Similar Time Series Modeling(World Scientific Publ Co Pte Ltd, 2020) Baleanu, Dumitru; Karaca, YelizIt 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 complex systems and structures are generally volatile, vulnerable and vague. Thus, analysis of the dynamics of occurrence of time section accurately, efficiently and timely is at the forefront to perform forecasting of volatile states of an economic environment which is a complex system in itself since it includes interrelated elements interacting with one another. To manage data selection effectively and attain robust prediction, characterizing complexity and self-similarity is critical in financial decision-making. Our study aims to obtain analyzes based on two main approaches proposed related to seven recognized indexes belonging to prominent countries (DJI, FCHI, GDAXI, GSPC, GSTPE, N225 and Bitcoin index). The first approach includes the employment of Hurst exponent (HE) as calculated by Rescaled Range (R/S) fractal analysis and Wavelet Entropy (WE) in order to enhance the prediction accuracy in the long-term trend in the financial markets. The second approach includes Artificial Neural Network (ANN) algorithms application Feed forward back propagation (FFBP), Cascade Forward Back Propagation (CFBP) and Learning Vector Quantization (LVQ) algorithm for forecasting purposes. The following steps have been administered for the two aforementioned approaches: (i) HE and WE were applied. Consequently, new indicators were calculated for each index. By obtaining the indicators, the new dataset was formed and normalized by min-max normalization method' (ii) to form the forecasting model, ANN algorithms were applied on the datasets. Based on the experimental results, it has been demonstrated that the new dataset comprised of the HE and WE indicators had a critical and determining direction with a more accurate level of forecasting modeling by the ANN algorithms. Consequently, the proposed novel method with multifarious methodology illustrates a new frontier, which could be employed in the broad field of various applied sciences to analyze pressing real-world problems and propose optimal solutions for critical decision-making processes in nonlinear, complex and dynamic environments.