Neural Computing and Applications, ISSN 0941-0643, 7/2017, Volume 28, Issue 7, pp. 1591 - 1610

In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm–Volterra...

Data Mining and Knowledge Discovery | Reproducing kernel Hilbert space method | 47B32 | Fuzzy integrodifferential equations | Computational Science and Engineering | Strongly generalized differentiability | Computational Biology/Bioinformatics | Gram–Schmidt process | Computer Science | Image Processing and Computer Vision | 34K28 | Artificial Intelligence (incl. Robotics) | 46S40 | Probability and Statistics in Computer Science | EXISTENCE | SYSTEM | Gram-Schmidt process | INCLUSIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | UNIQUENESS | NUMERICAL-SOLUTION | TURNING-POINT PROBLEMS | GLOBAL-SOLUTIONS | Annealing | Algorithms

Data Mining and Knowledge Discovery | Reproducing kernel Hilbert space method | 47B32 | Fuzzy integrodifferential equations | Computational Science and Engineering | Strongly generalized differentiability | Computational Biology/Bioinformatics | Gram–Schmidt process | Computer Science | Image Processing and Computer Vision | 34K28 | Artificial Intelligence (incl. Robotics) | 46S40 | Probability and Statistics in Computer Science | EXISTENCE | SYSTEM | Gram-Schmidt process | INCLUSIONS | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | UNIQUENESS | NUMERICAL-SOLUTION | TURNING-POINT PROBLEMS | GLOBAL-SOLUTIONS | Annealing | Algorithms

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 6, pp. 1243 - 1261

Latterly, many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, to a series of...

Time-fractional partial differential equations | Reproducing kernel Hilbert space method | Neumann boundary conditions | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher’s, and Newell–Whitehead) equations | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher's, and Newell–Whitehead) equations | FOKKER-PLANCK EQUATION | SYSTEM | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker-Planck, Fisher's, and Newell-Whitehead)equations | MATHEMATICS, APPLIED | VOLTERRA INTEGRAL-EQUATIONS | TURNING-POINT PROBLEMS | SUBDIFFUSION EQUATION | NUMERICAL ALGORITHM | SCHEMES | Methods | Numerical analysis | Differential equations

Time-fractional partial differential equations | Reproducing kernel Hilbert space method | Neumann boundary conditions | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher’s, and Newell–Whitehead) equations | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker–Planck, Fisher's, and Newell–Whitehead) equations | FOKKER-PLANCK EQUATION | SYSTEM | (Heat, cable, anomalous subdiffusion, reaction subdiffusion, Fokker-Planck, Fisher's, and Newell-Whitehead)equations | MATHEMATICS, APPLIED | VOLTERRA INTEGRAL-EQUATIONS | TURNING-POINT PROBLEMS | SUBDIFFUSION EQUATION | NUMERICAL ALGORITHM | SCHEMES | Methods | Numerical analysis | Differential equations

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 11/2018, Volume 94, Issue 3, pp. 1819 - 1834

This paper introduces an efficient numerical algorithm for solving a significant class of linear and nonlinear time-fractional partial differential equation...

Engineering | Vibration, Dynamical Systems, Control | Robin functions types | Classical Mechanics | Partial integrodifferential equation | Automotive Engineering | Hilbert space | Mechanical Engineering | Fractional modeling | Fredholm–Volterra operator | MECHANICS | Fredholm-Volterra operator | TURNING-POINT PROBLEMS | ALGORITHM | REPRODUCING KERNEL-METHOD | SYSTEMS | ENGINEERING, MECHANICAL | Models | Algorithms | Differential equations | Orthonormal functions | Operators (mathematics) | Error analysis | Numerical analysis | Partial differential equations | Functional analysis

Engineering | Vibration, Dynamical Systems, Control | Robin functions types | Classical Mechanics | Partial integrodifferential equation | Automotive Engineering | Hilbert space | Mechanical Engineering | Fractional modeling | Fredholm–Volterra operator | MECHANICS | Fredholm-Volterra operator | TURNING-POINT PROBLEMS | ALGORITHM | REPRODUCING KERNEL-METHOD | SYSTEMS | ENGINEERING, MECHANICAL | Models | Algorithms | Differential equations | Orthonormal functions | Operators (mathematics) | Error analysis | Numerical analysis | Partial differential equations | Functional analysis

Journal Article

Soft Computing, ISSN 1432-7643, 12/2017, Volume 21, Issue 23, pp. 7191 - 7206

In this paper, we investigate the analytic and approximate solutions of second-order, two-point fuzzy boundary value problems based on the reproducing kernel...

Engineering | Computational Intelligence | Gram–Schmidt process | Control, Robotics, Mechatronics | Reproducing kernel theory | Artificial Intelligence (incl. Robotics) | Fuzzy boundary value problems | Mathematical Logic and Foundations | Strongly generalized differentiability | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Gram-Schmidt process | TURNING-POINT PROBLEMS | DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms

Engineering | Computational Intelligence | Gram–Schmidt process | Control, Robotics, Mechatronics | Reproducing kernel theory | Artificial Intelligence (incl. Robotics) | Fuzzy boundary value problems | Mathematical Logic and Foundations | Strongly generalized differentiability | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Gram-Schmidt process | TURNING-POINT PROBLEMS | DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algorithms

Journal Article

Neural Computing and Applications, ISSN 0941-0643, 3/2018, Volume 29, Issue 5, pp. 1465 - 1479

This paper presents iterative reproducing kernel algorithm for obtaining the numerical solutions of Bagley–Torvik and Painlevé equations of fractional order....

Bagley–Torvik equation | 34B15 | 35F10 | Reproducing kernel algorithm | Fourier series expansion | Data Mining and Knowledge Discovery | 47B32 | Computational Science and Engineering | 34A08 | Computational Biology/Bioinformatics | Computer Science | Image Processing and Computer Vision | Painlevé equation | Artificial Intelligence (incl. Robotics) | Fractional-order derivative | Probability and Statistics in Computer Science | Algorithms

Bagley–Torvik equation | 34B15 | 35F10 | Reproducing kernel algorithm | Fourier series expansion | Data Mining and Knowledge Discovery | 47B32 | Computational Science and Engineering | 34A08 | Computational Biology/Bioinformatics | Computer Science | Image Processing and Computer Vision | Painlevé equation | Artificial Intelligence (incl. Robotics) | Fractional-order derivative | Probability and Statistics in Computer Science | Algorithms

Journal Article

Entropy, ISSN 1099-4300, 12/2013, Volume 15, Issue 12, pp. 5305 - 5323

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using...

Fractional differential equations | Fractional power series | Caputo fractional derivative | PHYSICS, MULTIDISCIPLINARY | DIFFERENTIAL-EQUATIONS | TSALLIS | DIFFUSION | DERIVATIVES | ENTROPY

Fractional differential equations | Fractional power series | Caputo fractional derivative | PHYSICS, MULTIDISCIPLINARY | DIFFERENTIAL-EQUATIONS | TSALLIS | DIFFUSION | DERIVATIVES | ENTROPY

Journal Article

Neural Computing and Applications, ISSN 0941-0643, 10/2018, Volume 30, Issue 8, pp. 2595 - 2606

Many problems arising in different fields of sciences and engineering can be reduced, by applying some appropriate discretization, either to a system of...

Temporal boundary value problems | Integrodifferential algebraic systems | Reproducing kernel theory | Volterra operator | PARTIAL-DIFFERENTIAL-EQUATION | VOLTERRA INTEGRAL-EQUATIONS | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SPACE | TURNING-POINT PROBLEMS | REPRODUCING KERNEL-METHOD | PADE SERIES | NONCLASSICAL CONDITIONS | SOLVING 2-POINT | Analysis | Methods | Algorithms

Temporal boundary value problems | Integrodifferential algebraic systems | Reproducing kernel theory | Volterra operator | PARTIAL-DIFFERENTIAL-EQUATION | VOLTERRA INTEGRAL-EQUATIONS | ALGORITHM | BOUNDARY-VALUE-PROBLEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | SPACE | TURNING-POINT PROBLEMS | REPRODUCING KERNEL-METHOD | PADE SERIES | NONCLASSICAL CONDITIONS | SOLVING 2-POINT | Analysis | Methods | Algorithms

Journal Article

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 2/2019, Volume 59, Issue 1, pp. 227 - 243

In this article, we propose and analyze an efficient computational algorithm for the numerical solutions of singular Fredholm time-fractional partial...

Computational Mathematics and Numerical Analysis | Fredholm operator | Mathematics of Computing | Reproducing kernel algorithm | Mathematical and Computational Engineering | Mathematics | Theory of Computation | Fractional calculus theory | Singular partial integrodifferential equation | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Annealing | Analysis | Algorithms | Nonlinear equations | Error analysis | Computer simulation | Infinite series | Simulated annealing | Dirichlet problem

Computational Mathematics and Numerical Analysis | Fredholm operator | Mathematics of Computing | Reproducing kernel algorithm | Mathematical and Computational Engineering | Mathematics | Theory of Computation | Fractional calculus theory | Singular partial integrodifferential equation | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Annealing | Analysis | Algorithms | Nonlinear equations | Error analysis | Computer simulation | Infinite series | Simulated annealing | Dirichlet problem

Journal Article

Soft Computing, ISSN 1432-7643, 8/2016, Volume 20, Issue 8, pp. 3283 - 3302

Modeling of uncertainty differential equations is very important issue in applied sciences and engineering, while the natural way to model such dynamical...

Engineering | Computational Intelligence | Gram–Schmidt process | Control, Robotics, Mechatronics | Reproducing kernel Hilbert space method | Artificial Intelligence (incl. Robotics) | Mathematical Logic and Foundations | Strongly generalized differentiability | Fuzzy differential equations | SYSTEM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Gram-Schmidt process | TURNING-POINT PROBLEMS | BOUNDARY-VALUE-PROBLEMS | INTEGRODIFFERENTIAL EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Methods | Differential equations | Resveratrol

Engineering | Computational Intelligence | Gram–Schmidt process | Control, Robotics, Mechatronics | Reproducing kernel Hilbert space method | Artificial Intelligence (incl. Robotics) | Mathematical Logic and Foundations | Strongly generalized differentiability | Fuzzy differential equations | SYSTEM | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Gram-Schmidt process | TURNING-POINT PROBLEMS | BOUNDARY-VALUE-PROBLEMS | INTEGRODIFFERENTIAL EQUATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Methods | Differential equations | Resveratrol

Journal Article

Mathematical Problems in Engineering, ISSN 1024-123X, 6/2015, Volume 2015, pp. 1 - 13

The reproducing kernel algorithm is described in order to obtain the efficient analytical-numerical solutions to nonlinear systems of two point, second-order...

EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TURNING-POINT PROBLEMS | POSITIVE SOLUTIONS | Boundary value problems | Usage | Complex systems | Analysis | Kernels | Nonlinear dynamics | Algorithms | Approximation | Mathematical analysis | Mathematical models | Dynamical systems

EQUATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | TURNING-POINT PROBLEMS | POSITIVE SOLUTIONS | Boundary value problems | Usage | Complex systems | Analysis | Kernels | Nonlinear dynamics | Algorithms | Approximation | Mathematical analysis | Mathematical models | Dynamical systems

Journal Article

Mathematical Problems in Engineering, ISSN 1024-123X, 4/2013, Volume 2013, pp. 1 - 10

In this paper, reproducing kernel Hilbert space method is applied to approximate the solution of two-point boundary value problems for fourth-order...

SYSTEM | REPRESENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Series | Boundary value problems | Hilbert space | Convergence (Mathematics) | Research | Mathematical research | Error analysis | Partial differential equations | Boundary conditions | Mathematical functions | Cybernetics | Genetic algorithms | Numerical analysis | Applied mathematics | Mathematical analysis | Integral equations | Error detection | Kernels | Approximation | Computation | Norms | Mathematical models

SYSTEM | REPRESENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | Series | Boundary value problems | Hilbert space | Convergence (Mathematics) | Research | Mathematical research | Error analysis | Partial differential equations | Boundary conditions | Mathematical functions | Cybernetics | Genetic algorithms | Numerical analysis | Applied mathematics | Mathematical analysis | Integral equations | Error detection | Kernels | Approximation | Computation | Norms | Mathematical models

Journal Article

Entropy, ISSN 1099-4300, 01/2014, Volume 16, Issue 1, pp. 471 - 493

The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of...

Multiple solutions | Fractional differential equations | Residual power series | DISSIPATION | PHYSICS, MULTIDISCIPLINARY | CONVECTION | residual power series | EQUATIONS | TSALLIS | fractional differential equations | FLOW | CHANNEL | DIFFUSION | multiple solutions | DERIVATIVES | ENTROPY | Boundary value problems | Mathematical analysis | Convection modes | Nonlinearity | Mathematical models | Computational efficiency | Convection | Heat transfer | power series

Multiple solutions | Fractional differential equations | Residual power series | DISSIPATION | PHYSICS, MULTIDISCIPLINARY | CONVECTION | residual power series | EQUATIONS | TSALLIS | fractional differential equations | FLOW | CHANNEL | DIFFUSION | multiple solutions | DERIVATIVES | ENTROPY | Boundary value problems | Mathematical analysis | Convection modes | Nonlinearity | Mathematical models | Computational efficiency | Convection | Heat transfer | power series

Journal Article

Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 09/2018, Volume 34, Issue 5, pp. 1759 - 1780

The subject of the fractional calculus theory has gained considerable popularity and importance due to their attractive applications in widespread fields of...

time‐fractional partial differential equations | Dirichlet functions types | reproducing kernel algorithm | Tricomi equation | Keldysh equation | time-fractional partial differential equations | MATHEMATICS, APPLIED | TURNING-POINT PROBLEMS | BOUNDARY-VALUE-PROBLEMS | SUBJECT | INTEGRODIFFERENTIAL EQUATIONS | NUMERICAL ALGORITHM | Algorithms | Error analysis | Computer simulation | Infinite series | Dirichlet problem | Mathematical models | Hilbert space | Fractional calculus

time‐fractional partial differential equations | Dirichlet functions types | reproducing kernel algorithm | Tricomi equation | Keldysh equation | time-fractional partial differential equations | MATHEMATICS, APPLIED | TURNING-POINT PROBLEMS | BOUNDARY-VALUE-PROBLEMS | SUBJECT | INTEGRODIFFERENTIAL EQUATIONS | NUMERICAL ALGORITHM | Algorithms | Error analysis | Computer simulation | Infinite series | Dirichlet problem | Mathematical models | Hilbert space | Fractional calculus

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 7/2013, Volume 2013, pp. 1 - 10

A new analytic method is applied to singular initial-value Lane-Emden-type problems, and the effectiveness and performance of the method is studied. The...

MATHEMATICS, APPLIED | APPROXIMATE SOLUTION | 1ST INTEGRALS | DIFFERENTIAL-EQUATION | ALGORITHM | Research | Differential equations, Partial | Mathematical research | Series, Taylor's | Studies | Ordinary differential equations | Algorithms | Numerical analysis | Astrophysics | Methods | Computation | Mathematical analysis | Exact solutions | Mathematical models | Polynomials | Representations | Computational efficiency | Handling

MATHEMATICS, APPLIED | APPROXIMATE SOLUTION | 1ST INTEGRALS | DIFFERENTIAL-EQUATION | ALGORITHM | Research | Differential equations, Partial | Mathematical research | Series, Taylor's | Studies | Ordinary differential equations | Algorithms | Numerical analysis | Astrophysics | Methods | Computation | Mathematical analysis | Exact solutions | Mathematical models | Polynomials | Representations | Computational efficiency | Handling

Journal Article

Discrete Dynamics in Nature and Society, ISSN 1026-0226, 2014, Volume 2014

A new kind of optimization technique, namely, continuous genetic algorithm, is presented in this paper for numerically approximating the solutions of Troesch's...

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | 2ND-ORDER | Functions, Continuous | Research | Mathematical research | Differential equations | Genetic algorithms | Digital computers | Problems | Numerical analysis | Applied mathematics | Colleges & universities | Science | Ordinary differential equations | Optimization techniques | Boundary conditions | Models | Mathematics | Methods | Algorithms | Approximation | Dynamics | Mathematical analysis | Mathematical models | Derivatives | Optimization

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | 2ND-ORDER | Functions, Continuous | Research | Mathematical research | Differential equations | Genetic algorithms | Digital computers | Problems | Numerical analysis | Applied mathematics | Colleges & universities | Science | Ordinary differential equations | Optimization techniques | Boundary conditions | Models | Mathematics | Methods | Algorithms | Approximation | Dynamics | Mathematical analysis | Mathematical models | Derivatives | Optimization

Journal Article

Discrete Dynamics in Nature and Society, ISSN 1026-0226, 12/2013, Volume 2013, pp. 1 - 12

In this article, a new analytical method has been devised to solve higher-order initial value problems for ordinary differential equations. This method was...

LIENARD EQUATION | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DECOMPOSITION METHOD | MULTIDISCIPLINARY SCIENCES | EXPLICIT EXACT-SOLUTIONS | DYNAMICS | Boundary value problems | Convergence (Mathematics) | Research | Mathematical research | Series, Taylor's | Construction

LIENARD EQUATION | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DECOMPOSITION METHOD | MULTIDISCIPLINARY SCIENCES | EXPLICIT EXACT-SOLUTIONS | DYNAMICS | Boundary value problems | Convergence (Mathematics) | Research | Mathematical research | Series, Taylor's | Construction

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 09/2012, Volume 2012, pp. 1 - 16

This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The...

SYSTEM | BOUNDARY-VALUE-PROBLEMS | REPRESENTATION | MATHEMATICS, APPLIED | ALGORITHM | Studies | Models | Algorithms | Finite element analysis | Fluid dynamics | Intervals | Kernels | Approximation | Mathematical analysis | Exact solutions | Nonlinearity | Mathematical models | Derivatives

SYSTEM | BOUNDARY-VALUE-PROBLEMS | REPRESENTATION | MATHEMATICS, APPLIED | ALGORITHM | Studies | Models | Algorithms | Finite element analysis | Fluid dynamics | Intervals | Kernels | Approximation | Mathematical analysis | Exact solutions | Nonlinearity | Mathematical models | Derivatives

Journal Article