<abstract><title style='display:none'>Abstract</title> In this study, a numerical solution of the modified Burgers’ equation is obtained by the finite difference methods. For the solution process, two linearization techniques have been applied to get over the non-linear term existing in the equation. Then, some comparisons have been made between the obtained results and those available in the literature. Furthermore, the error norms L2 and L∞ are computed and found to be sufficiently small and compatible with others in the literature. The stability analysis of the linearized finite difference equations obtained by two different linearization techniques has been separately conducted via Fourier stability analysis method.</abstract>

Numerical Solutions of the Modified Burgers’ Equation by Finite Difference Methods

<abstract xml:lang="en"><title style='display:none'>Diagonal Scaling of Ill-Conditioned Matrixes by Genetic Algorithm</title>The purpose of this article is to use genetic algorithm for finding two invertible diagonal matrices <italic>D</italic>1 and <italic>D</italic>2 such that the scaled matrix <italic>D</italic>1<italic>AD</italic>2 approaches to minimum condition number.</abstract>

Diagonal Scaling of Ill-Conditioned Matrixes by Genetic Algorithm

<abstract><title style='display:none'>Abstract</title>In recent years, a lot of effort has been put into finding suitable mathematical models that fit historical data set. Such models often include coefficients and the accuracy of data approximation depends on them. So the goal is to choose the unknown coefficients to achieve the best possible approximation of data by the corresponding solution of the model. One of the standard methods for coefficient estimation is the least square method. This can provide us data approximation but it can also serve as a starting method for further minimizations such as Matlab function fminsearch.</abstract>

Data approximation using Lotka-Volterra models and a software minimization function

<abstract><title style='display:none'>Abstract</title>The use of geometrical methods in statistics has a long and rich history highlighting many different aspects. These methods are usually based on a Riemannian structure defined on the space of parameters that characterize a family of probabilities. In this paper, we consider the finite dimensional case but the basic ideas can be extended similarly to the infinite-dimensional case. Our aim is to understand exponential families of probabilities on a finite set from an intrinsic geometrical point of view and not through the parameters that characterize some given family of probabilities.For that purpose, we consider a Riemannian geometry defined on the set of positive vectors in a finite-dimensional space. In this space, the probabilities on a finite set comprise a submanifold in which exponential families correspond to geodesic surfaces. We shall also obtain a geometric/dynamic interpretation of Jaynes’ method of maximum entropy.</abstract>

Geometry of the probability simplex and its connection to the maximum entropy method

<abstract><title style='display:none'>Abstract</title>Conformable fractional complex transform is introduced in this paper for converting fractional partial differential equations to ordinary differential equations. Hence analytical methods in advanced calculus can be used to solve these equations. Conformable fractional complex transform is implemented to fractional partial differential equations such as space fractional advection diffusion equation and space fractional telegraph equation to obtain the exact solutions of these equations.</abstract>

Department of Mathematics, Faculty of Science, Selçuk University, Konya,

Department of Mathematics, Faculty of Science and Art, Mustafa Kemal University, Hatay,

New Fractional Complex Transform for Conformable Fractional Partial Differential Equations

<abstract><title style='display:none'>Abstract</title>Motivated by the substantial development in the theory of digamma function, we derive some new identities for the digamma function. These new identities enable us to compute the values of the digamma function for fractional orders in an analogous manner. Also, we mention two errata, found in Jensen’s article (An elementary exposition of the theory of the Gamma function, 1916), and present their correct forms.</abstract>

Analytic computation of digamma function using some new identities

<abstract>
<title style='display:none'>Abstract</title>
This paper analyses the <italic>M</italic>/<italic>M</italic>(<italic>a</italic>,<italic>b</italic>)/1/<italic>MWV</italic> queuing model with various types of breakdowns. During peak times, the system has breakdown due to server unavailability. The model considers system with two types of breakdowns. The system may breakdown in two different ways during busy and working vacation stages. Customer arrives to the system with parameter <italic>λv </italic>which follows Poisson distribution and server provides service in regular busy period with parameter <italic>µrb </italic>and under the multiple working vacations it provides service with parameter <italic>µwv </italic>with exponential distribution. In this model batches of customers are served under General Bulk Service Rule. The system may breakdown at any time. The breakdown that occurs during working vacation is denoted as <italic>βv</italic>1 and the breakdown during busy state is denoted as <italic>βv</italic>2. The steady-state equation, the performance of measures for the system and particular cases of described model are derived. Finally, a real life example demonstrated the validity of the model in a proper way.
</abstract>

Performance study of the <italic>M</italic>/<italic>M</italic>(<italic>a</italic>,<italic>b</italic>)/1/<italic>MWV</italic> queuing system with types of breakdowns

<abstract>
<title style='display:none'>Abstract</title>
The foremost target of the proposed work focuses on establishing fixed point theorems for the new concept named Intuitionistic fuzzy cone-b metric space (in short IFCbMS). Various definitions like compatible mappings, weakly-compatible maps (WC maps) and E.A. property are also used to prove new results for IFCbMS. The proofs of fixed points for FMS, IFMS, NFMS in the setting of E.A. property are taken as base for this research. Examples mentioned in the paper are increasing the importance of the research done. An application is also given to show the importance of the result proved. The application of this paper leads to the solution of an integral equation in context of implicit functions.
</abstract>

Some new fixed point results in Intuitionistic fuzzy cone-b metric spaces

<abstract>
<title style='display:none'>Abstract</title>
In this article, we present a novel approach to measuring inaccuracy, introducing a two-parametric weighted generalized inaccuracy measure of order <italic>α</italic> and type <italic>β</italic>, along with its residual version. Our proposed measure depends on the proportional hazard rate model (PHRM) to uniquely determine the survival function, and we have derived a characterization result for this measure. Through our analysis under the PHRM framework, we have studied various properties of the proposed measure and their interrelationships.
</abstract>

A new two-parametric weighted generalized inaccuracy measure

<abstract>
<title style='display:none'>Abstract</title>
The notion of Plithogenic vertex domination and Plithogenic edge domination in Plithogenic product fuzzy graphs (PPFGs) has been newly introduced and discussed based on P-weights of P-vertices and P-edges respectively with properties, results and examples. Plithogenic vertex domination number and Plithogenic edge domination number for a Plithogenic product fuzzy graph (PPFG), and the bounds and algorithms for and the maximum and minimum values and algorithms for the same are also investigatedthe same are also investigated. Perfect Plithogenic vertex domination and perfect Plithogenic edge domination are presented as special cases of Plithogenic vertex domination and Plithogenic edge domination respectively. It is observed that the P-vertex (P-edge) with the maximum P-weight exists in every Plithogenic vertex (edge) dominating set of a Plithogenic product fuzzy graph. The novelty in these ideas of domination is that a better perception of reality can be obtained through the analysis of both, Plithogenic vertex domination and Plithogenic edge domination, in any Plithogenic product fuzzy graphical structure.
</abstract>

Domination in Plithogenic product fuzzy graphs

<abstract>
<title style='display:none'>Abstract</title>
The use of credit for various occasions has become a routine in our lives. In return, banking and financial institutions require to determine whether the loan demands from them contain any risk. Accordingly, these institutions have been increased their activities in determining whether credit rating models from past credit records of the person applying for the loan works properly. Machine learning-based technologies have opened a new era in this field. AI and machine learning based methods for credit scoring are currently implemented by banking or non-banking financial institutions. Employed models are to extract meaningful features from the required data in which wide variety of information available. In this study, credit risk assessment is conducted using boosting methods such as CatBoost, XGBoost and Light GBM. To this aim, Kaggle Home Credit Default Risk dataset is used and the effect of crediting tendency on the results is also considered. The results have shown that gradient boosting methods provide results that are close to each other, and crediting tendency produces better AUC score in CatBoost while it causes a small decrement in AUC score of XGBoost and LightGBM.
</abstract>

Credit risk analysis using boosting methods

<abstract>
<title style='display:none'>Abstract</title>
A new Lomax Rayleigh distribution (NLRD) is proposed and generated using Transformed Transformer (T-X) family generator. Various structural properties like generating functions, moments, limiting form, quantile function median and mode of NLRD are studied. Maximum likelihood estimators (MLEs) of the parameters are obtained and the model fitting is tested with simulated data. Model adequacy with live data is explained with two real-time cancer data sets. The NLRD shows a better fit in the estimation of survival in bile duct cancer and head and neck cancer data than other existing distributions.
</abstract>

Survival analysis of cancer patients using a new Lomax Rayleigh distribution

<abstract><title style='display:none'>Abstract</title> In this paper, we establish Hermite-Hadamard type inequalities for s - convex functions in the second sense and m - convex functions via fractional integrals. The analysis used in the proofs is fairly elementary. </abstract>

Department of Mathematics, Faculty of Science and Arts, Ordu University, Ordu, TURKEY

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, TURKEY

Department of Mathematics K. K. Education Faculty, Ataturk University, 25640, Kampus, Erzurum, TURKEY

Department of Mathematics, Faculty of Science and Arts, Kahramanmaraş Sütcü Imam University, Kahramanmaraş-TURKEY

The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results

<abstract><title style='display:none'>Abstract</title> In this note, we obtain new some inequalities of Simpson’s type based on convexity. Some applications for special means of real numbers are also given.</abstract>

Department of Mathematics, Faculty of Science and Arts, Duzce University, Duzce, Turkey

Ataturk University, K.K. Education Faculty, Department of Mathematics, 25240, Campus, Erzurum, Turkey

On New Inequalities of Simpson’s Type for Functions Whose Second Derivatives Absolute Values are Convex

<abstract><title style='display:none'>Abstract</title>The paper presents design, background and experimental results of the IPTables applied in IPv4 and IP6Tables applied in IPv6 network compared through several tested parameters. The experimental testbed environment is based on P2P grid utilized for DDoS attacks. IPTables tool is used for packet filtering and consequently for preventing DoS/DDoS attacks. It allows a system administrator to configure the tables, the chains and rules it stores in order to manage the incoming and outgoing packets. The packets are treated according to the rules’ results provided by the packet processing. A rule in a chain can be bound with another chain in the table etc.We employ the P2P grid environment to carry out as well as to coordinate DDoS attack on the availability of services to simulate real DDoS attack launched indirectly through many compromised computing systems. The same routing protocols as well as the same firewall rules were used for IPv4 and for IPv6 network. The main aim was to analyse pros and cons of new IP6Tables tool compared with IPTables in IPv4 networks in light of the resistance to DDoS attacks which is still one of the most significant threats in the IPv6 networks.</abstract>

Department of Applied Informatics and Mathematics, University of SS. Cyril and Methodius, Slovak Republic

Performance Evaluations of IPTables Firewall Solutions under DDoS attacks

<abstract><title style='display:none'>Abstract</title> In this paper, Riemann-Liouville type fractional integral identity and inequality for differentiable convex mappings are studied. Some applications to special means of real numbers are given. Finally, error estimates for a midpoint formula are also obtained.</abstract>

Department of Mathematics, Guizhou University Guiyang, Guizhou 550025, P.R. China

Department of Mathematical Analysis and Numerical Mathematics Faculty of Mathematics, Physics and Informatics Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia

Department of Mathematics Guizhou University Guiyang, Guizhou 550025, P.R. China

Fractional Integral Inequalities for Differentiable Convex Mappings and Applications to Special Means and a Midpoint Formula

<abstract><title style='display:none'>Abstract</title>In this work, we apply fractional calculus to analyze a class of economic growth modelling (EGM) of the Spanish economy. More precisely, the Grünwald-Letnnikov and Caputo derivatives are used to simulate GDP by replacing the previous integer order derivatives with the help of Matlab, SPSS and R software. As a result, we find that the data raised from the Caputo derivative are better than the data raised from the Grünwald-Letnnikov derivative. We improve the previous result in [12].</abstract>

Applying Fractional Calculus to Analyze Economic Growth Modelling

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