Numerical solution of fractional elliptic PDE\u27s by the collocation method

In this presentation a numerical solution for the solution of fractional order of elliptic partial differential equation in R2 is proposed. In this method we use the Radial basis functions (RBFs) method to benefit the desired properties of mesh free techniques such as no need to generate any mesh and easily applied to multi dimensions. In the numerical solution approach the RBF collocation method is used to discrete fractional derivative terms with the Gaussian basis function. Two dimensional numerical examples are presented and discussed, which conform well with the corresponding exact solutions

Some Improvements of Conformable Fractional Integral Inequalities

In this study, we wish to set up and present some new conformable fractional integral inequalities of the Gronwall type which have a great variety of implementation area in differential and integral equations

ON BIVARIATE RETARDED INTEGRAL INEQUALITIES AND THEIR APPLICATIONS

In this paper, we obtain some retarded integral inequalities in two independent variables which can be used as tools in the theory of partial differential and integral equations with time delays. The presented inequalities are of new forms compared with the existing ones so far in the literature. In order to illustrate the validity of the theorems we give one application for them for the solution to certain fractional order differential equations

An End-to-end Neural Natural Language Interface for Databases

The ability to extract insights from new data sets is critical for decision making. Visual interactive tools play an important role in data exploration since they provide non-technical users with an effective way to visually compose queries and comprehend the results. Natural language has recently gained traction as an alternative query interface to databases with the potential to enable non-expert users to formulate complex questions and information needs efficiently and effectively. However, understanding natural language questions and translating them accurately to SQL is a challenging task, and thus Natural Language Interfaces for Databases (NLIDBs) have not yet made their way into practical tools and commercial products. In this paper, we present DBPal, a novel data exploration tool with a natural language interface. DBPal leverages recent advances in deep models to make query understanding more robust in the following ways: First, DBPal uses a deep model to translate natural language statements to SQL, making the translation process more robust to paraphrasing and other linguistic variations. Second, to support the users in phrasing questions without knowing the database schema and the query features, DBPal provides a learned auto-completion model that suggests partial query extensions to users during query formulation and thus helps to write complex queries

Numerical analysis of fractional Volterra integral equations via Bernstein approximation method

In this study, Bernstein approximation method has been applied along with Riemann-Liouville fractional integral operator to solve both the second and the first kind of fractional Volterra integral equations (2nd FVIEs and 1st FVIEs respectively). In order to show the applicability and efficiency of the proposed technique, some convergence analysis has been provided. Illustrative numerical experiments with comparison are included to indicate the validity and practicability of the method. All of the numerical calculation in this research has been done on a personal computer implementing some programs written in MATLAB. (C) 2020 Elsevier B.V. All rights reserved.WOS:0005828024000252-s2.0-8509125228

On New Modification of Bernstein Operators: Theory and Applications

Approximation theory has a significant place in the studies in mathematics, and the researches on it are increasing with each passing day. Accordingly, a number of studies have been presented about Bernstein approximation which is one of the most known linear positive operators. In this study, a new modification of Bernstein operators which fix constant and preserve Korovkin's other test functions in limit case has been introduced. Then, the approximation properties of the newly defined operators such as asymptotic formulas, weighted approximation and rate of convergence have been presented. Moreover, numerical simulations are included. Finally, discussion and conclusions are presented.WOS:0005554957000022-s2.0-8508809199

Approximation of functions with linear positive operators which fix {1, phi} and {1, phi(2)}

In this manuscript, linear and positive operators described on bounded and unbounded intervals that fix the function sets {1, phi} and {1, phi(2)} such that phi is an element of C[0, 1] are presented. Then we present different types of operators by choosing different functions and values. Finally, Voronovskaya type theorems are given for this newly defined sequences of linear and positive operators.WOS:0006046116000142-s2.0-8508810678

On approximation properties of a new construction of Baskakov operators

The purpose of this research is to construct sequences of Baskakov operators such that their construction consists of a function sigma by use of two function sequences, xi n and eta n. In these operators, sigma not only features the sequences of operators but also features the Korovkin function set {1,sigma,sigma(2)} in a weighted function space such that the operators fix exactly two functions from the set. Thereafter, weighted uniform approximation on an unbounded interval, the degree of approximation with regards to a weighted modulus of continuity, and an asymptotic formula of the new operators are presented. Finally, some illustrative results are provided in order to observe the approximation properties of the newly defined Baskakov operators. The results demonstrate that the introduced operators provide better results in terms of the rate of convergence according to the selection of sigma.WOS:0006530387000012-s2.0-8510696119

Approximating the Finite Hilbert Transform for Absolutely Continuous Mappings and Applications in Numerical Integration

WOS: 000441924900001The finite Hilbert transform is a practical instrument in the field of signal processing, time series analysis, radar systems, and other fields of the engineering sciences. In this study, some explicit bounds for the finite Hilbert transform are given utilizing the fundamental integral identity for absolutely continuous mappings