Advances in Difference Equations, ISSN 1687-1839, 12/2013, Volume 2013, Issue 1, pp. 1 - 16

... applications of the variational iteration method - from differential equations to q-fractional difference equations Guo-Cheng Wu 1,2* and Dumitru Baleanu 3,4,5...

fractional calculus | time scales | q -calculus | symbolic computation | Mathematics | variational iteration method | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Laplace transform | Partial Differential Equations | Variational iteration method | Q-calculus | Symbolic computation | Time scales | Fractional calculus | MATHEMATICS | MATHEMATICS, APPLIED | Q-INTEGRALS | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | DERIVATIVES | q-calculus | Linear systems | Usage | Difference equations | Innovations | Laplace transformation | Iterative methods (Mathematics) | Methods | Calculi | Mathematical analysis | Differential equations | Initial value problems | Calculus | Iterative methods | Concentrates

fractional calculus | time scales | q -calculus | symbolic computation | Mathematics | variational iteration method | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Laplace transform | Partial Differential Equations | Variational iteration method | Q-calculus | Symbolic computation | Time scales | Fractional calculus | MATHEMATICS | MATHEMATICS, APPLIED | Q-INTEGRALS | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | DERIVATIVES | q-calculus | Linear systems | Usage | Difference equations | Innovations | Laplace transformation | Iterative methods (Mathematics) | Methods | Calculi | Mathematical analysis | Differential equations | Initial value problems | Calculus | Iterative methods | Concentrates

Journal Article

Advances in difference equations, ISSN 1687-1847, 2013, Volume 2013, Issue 1, pp. 1 - 14

...), to solve a system of fractional nonlinear differential equations that arise in the model for HIV infection of CD4...

Ordinary Differential Equations | Functional Analysis | fractional order derivative | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | model for HIV infection of CD4 + T cells | attractor one-dimensional Keller-Segel equations | homotopy decomposition method | Partial Differential Equations | Attractor one-dimensional Keller-Segel equations | Homotopy decomposition method | Fractional order derivative | Model for HIV infection of CD4+ T cells | model for HIV infection of CD4(+) T cells | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICAL-ANALYSIS | DYNAMICS | T-CELLS

Ordinary Differential Equations | Functional Analysis | fractional order derivative | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | model for HIV infection of CD4 + T cells | attractor one-dimensional Keller-Segel equations | homotopy decomposition method | Partial Differential Equations | Attractor one-dimensional Keller-Segel equations | Homotopy decomposition method | Fractional order derivative | Model for HIV infection of CD4+ T cells | model for HIV infection of CD4(+) T cells | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICAL-ANALYSIS | DYNAMICS | T-CELLS

Journal Article

Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 04/2018, Volume 148, Issue 2, pp. 429 - 446

Set differential equations are usually formulated in terms of the Hukuhara differential...

ordinary differential equations in Banach spaces | existence and uniqueness | set differential equations | MATHEMATICS | MATHEMATICS, APPLIED | Uniqueness theorems | Differential calculus | Mathematical analysis | Existence theorems | Differential geometry | Differential equations | Ordinary differential equations | Set theory | Calculus | Banach spaces | Banach space

ordinary differential equations in Banach spaces | existence and uniqueness | set differential equations | MATHEMATICS | MATHEMATICS, APPLIED | Uniqueness theorems | Differential calculus | Mathematical analysis | Existence theorems | Differential geometry | Differential equations | Ordinary differential equations | Set theory | Calculus | Banach spaces | Banach space

Journal Article

1984, ISBN 0444876340, Volume 2., ix, 307

Book

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 9/2019, Volume 31, Issue 3, pp. 1341 - 1371

In this paper we study the Wong–Zakai approximations given by a stationary process via the Wiener shift and their associated long term pathwise behavior for the stochastic partial differential equations driven by a white noise...

Upper semicontinuity | Ordinary Differential Equations | Random attractor | Secondary 35B41 | Wong–Zakai approximation | Primary 35B40 | White noise | Mathematics | Applications of Mathematics | 37L30 | Partial Differential Equations | Stochastic equation | EXISTENCE | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | THEOREM | CHAOTIC BEHAVIOR | DRIVEN | INTEGRALS | MATHEMATICS | PULLBACK ATTRACTORS | CONVERGENCE | Wong-Zakai approximation

Upper semicontinuity | Ordinary Differential Equations | Random attractor | Secondary 35B41 | Wong–Zakai approximation | Primary 35B40 | White noise | Mathematics | Applications of Mathematics | 37L30 | Partial Differential Equations | Stochastic equation | EXISTENCE | EVOLUTION EQUATIONS | MATHEMATICS, APPLIED | THEOREM | CHAOTIC BEHAVIOR | DRIVEN | INTEGRALS | MATHEMATICS | PULLBACK ATTRACTORS | CONVERGENCE | Wong-Zakai approximation

Journal Article

1998, 5th ed., Universitext, ISBN 9783540637202, xix, 324

Book

2006, EMS textbooks in mathematics, ISBN 3037190175, viii, 377

Book

2004, 3rd ed., ISBN 0120415623, xvi, 876

Book

Journal of the American Statistical Association, ISSN 0162-1459, 10/2014, Volume 109, Issue 508, pp. 1672 - 1682

Existing estimation methods for ordinary differential equation (ODE) models are not applicable to discrete data...

Evolutionary hybrid algorithm | Influenza viral dynamics | Numerical error theory | Generalized nonlinear model | Simulations | Statistical variance | Time series models | Identifiability | Statistical models | Theory and Methods | Analytical estimating | Ordinary differential equations | Inference | Mathematical models | Estimation methods | MAXIMUM-LIKELIHOOD-ESTIMATION | PARAMETER-ESTIMATION | REGRESSION-MODELS | VARYING COEFFICIENTS | STATISTICS & PROBABILITY | INFLUENZA-A VIRUS | ADAPTIVE IMMUNE-RESPONSE | MEASUREMENT ERROR | DETERMINISTIC DYNAMIC-MODELS | CATEGORICAL TIME-SERIES | HIV-1 DYNAMICS

Evolutionary hybrid algorithm | Influenza viral dynamics | Numerical error theory | Generalized nonlinear model | Simulations | Statistical variance | Time series models | Identifiability | Statistical models | Theory and Methods | Analytical estimating | Ordinary differential equations | Inference | Mathematical models | Estimation methods | MAXIMUM-LIKELIHOOD-ESTIMATION | PARAMETER-ESTIMATION | REGRESSION-MODELS | VARYING COEFFICIENTS | STATISTICS & PROBABILITY | INFLUENZA-A VIRUS | ADAPTIVE IMMUNE-RESPONSE | MEASUREMENT ERROR | DETERMINISTIC DYNAMIC-MODELS | CATEGORICAL TIME-SERIES | HIV-1 DYNAMICS

Journal Article

Computational Mechanics, ISSN 0178-7675, 4/2019, Volume 63, Issue 4, pp. 713 - 723

Due to the merit of transforming fractional differential equations into ordinary differential equations, the Yuan and Agrawal method has gained a lot of research interests over the past decade...

Fractional differential equation | Engineering | Yuan–Agrawal method | Gauss–Laguerre rule | Classical and Continuum Physics | Convergence rate | Theoretical and Applied Mechanics | Computational Science and Engineering | Gauss-Laguerre rule | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Yuan-Agrawal method | Yuan (China) | Analysis | Methods | Differential equations

Fractional differential equation | Engineering | Yuan–Agrawal method | Gauss–Laguerre rule | Classical and Continuum Physics | Convergence rate | Theoretical and Applied Mechanics | Computational Science and Engineering | Gauss-Laguerre rule | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Yuan-Agrawal method | Yuan (China) | Analysis | Methods | Differential equations

Journal Article

Journal of Bioinformatics and Computational Biology, ISSN 0219-7200, 02/2014, Volume 12, Issue 1

In the systems biology field, algorithms for structural identification of ordinary differential equations (ODEs...

ordinary differential equations | System identification | BIOCHEMICAL NETWORK MODELS | PROFILES | PARAMETER-ESTIMATION | TIME-SERIES DATA | ALGORITHM | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | OPTIMIZATION | INFERENCE

ordinary differential equations | System identification | BIOCHEMICAL NETWORK MODELS | PROFILES | PARAMETER-ESTIMATION | TIME-SERIES DATA | ALGORITHM | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SYSTEMS | OPTIMIZATION | INFERENCE

Journal Article

2019, Algorithms and Computations in Mathematics, ISBN 303026453X, Volume 28

This book presents a series of lectures focusing on differential equations from viewpoints of formal calculus and geometry through applications of quiver theory...

Mathematics

Mathematics

Book

2005, Chapman & Hall/CRC applied mathematics and nonlinear science series, ISBN 1584883731, 671

An Introduction to Partial Differential Equations with MATLAB exposes the basic ideas critical to the study of PDEs-- characteristics, integral transforms, Green's functions, and, most importantly...

Differential equations, Partial | Computer-assisted instruction | MATLAB

Differential equations, Partial | Computer-assisted instruction | MATLAB

Book

TheScientificWorld, ISSN 1537-744X, 2013, Volume 2013, pp. 1 - 8

We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation...

PERIODIC-SOLUTIONS | ORDER | TRAVELING-WAVE SOLUTIONS | MULTIDISCIPLINARY SCIENCES | PERTURBATION TECHNIQUE | SYMBOLIC COMPUTATION | RICCATI EQUATION | NONLINEAR EVOLUTION-EQUATIONS | RATIONAL EXPANSION METHOD | (G'/G)-EXPANSION | Models, Theoretical | Algorithms | Numerical Analysis, Computer-Assisted | Computer Simulation | Functions, Exponential | Research | Differential equations, Partial | Mathematical research | Fluid mechanics | Transformation | Partial differential equations | Physics | Algebra | Applied mathematics | Mathematical analysis | Spacetime | Differential equations | Ordinary differential equations | Control theory | Power | Methods

PERIODIC-SOLUTIONS | ORDER | TRAVELING-WAVE SOLUTIONS | MULTIDISCIPLINARY SCIENCES | PERTURBATION TECHNIQUE | SYMBOLIC COMPUTATION | RICCATI EQUATION | NONLINEAR EVOLUTION-EQUATIONS | RATIONAL EXPANSION METHOD | (G'/G)-EXPANSION | Models, Theoretical | Algorithms | Numerical Analysis, Computer-Assisted | Computer Simulation | Functions, Exponential | Research | Differential equations, Partial | Mathematical research | Fluid mechanics | Transformation | Partial differential equations | Physics | Algebra | Applied mathematics | Mathematical analysis | Spacetime | Differential equations | Ordinary differential equations | Control theory | Power | Methods

Journal Article

2019, 2nd ed. 2019, ISBN 3030205053, 522

This book is designed to serve as a textbook for a course on ordinary differential equations, which is usually a required course in most science and engineering disciplines and follows calculus courses...

Engineering | Mathematical Methods in Physics | Ordinary Differential Equations | Engineering Mathematics

Engineering | Mathematical Methods in Physics | Ordinary Differential Equations | Engineering Mathematics

eBook

Nonlinear dynamics, ISSN 1573-269X, 2019, Volume 97, Issue 1, pp. 225 - 245

Two methods based on stochastic reduced-order models (SROM) are proposed to solve stochastic stable nonlinear ordinary differential equations...

Stochastic nonlinear dynamic equations | Stochastic reduced-order models | RANDOM VIBRATION | BOUC-WEN MODEL | Stochastic processes | UNCERTAINTY QUANTIFICATION | SIMULATION | ENGINEERING, MECHANICAL | MECHANICS | Response statistics | SYSTEMS | OPTIMIZATION | BIFURCATION | Extreme values | STATIONARY | Usage | Models | Analysis | Differential equations | Linear systems | Nonlinear equations | Degrees of freedom | Computer simulation | Random excitation | Probabilistic methods | Statistical methods | Reduced order models | Tessellation | Samples | Ordinary differential equations | Stochastic models | Nonlinear response | Nonlinear systems | Random vibration | Methods

Stochastic nonlinear dynamic equations | Stochastic reduced-order models | RANDOM VIBRATION | BOUC-WEN MODEL | Stochastic processes | UNCERTAINTY QUANTIFICATION | SIMULATION | ENGINEERING, MECHANICAL | MECHANICS | Response statistics | SYSTEMS | OPTIMIZATION | BIFURCATION | Extreme values | STATIONARY | Usage | Models | Analysis | Differential equations | Linear systems | Nonlinear equations | Degrees of freedom | Computer simulation | Random excitation | Probabilistic methods | Statistical methods | Reduced order models | Tessellation | Samples | Ordinary differential equations | Stochastic models | Nonlinear response | Nonlinear systems | Random vibration | Methods

Journal Article

1996, Lectures in mathematics ETH Zürich, ISBN 9783764353926, 152

Book

Advances in Difference Equations, ISSN 1687-1839, 12/2014, Volume 2014, Issue 1, pp. 1 - 12

In this paper, the authors study some growth properties of analytic functions of -order in the disc and apply them to investigating the growth and zeros of solutions of complex linear differential...

Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | unit disc | exponent of convergence of zero-sequence | Partial Differential Equations | linear differential equations | order | [p, q]-exponent of convergence of zero-sequence | [p, q]-order | Linear differential equations | Unit disc | MATHEMATICS | MATHEMATICS, APPLIED | GROWTH | Linear programming | Usage | Differential equations | Discs | Disks | Difference equations | Analytic functions | Mathematical analysis

Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Mathematics | unit disc | exponent of convergence of zero-sequence | Partial Differential Equations | linear differential equations | order | [p, q]-exponent of convergence of zero-sequence | [p, q]-order | Linear differential equations | Unit disc | MATHEMATICS | MATHEMATICS, APPLIED | GROWTH | Linear programming | Usage | Differential equations | Discs | Disks | Difference equations | Analytic functions | Mathematical analysis

Journal Article

Journal of dynamics and differential equations, ISSN 1572-9222, 2017, Volume 30, Issue 1, pp. 359 - 377

In this manuscript, we establish local exponential stability of the trivial solution of differential equations driven...

Ordinary Differential Equations | Secondary: 34A34 | Differential equations | Primary: 37L15 | Mathematics | Applications of Mathematics | Exponential stability | Fractional Brownian motion | 34F05 | Partial Differential Equations | Hölder continuous driving signal | MATHEMATICS | ERGODICITY | MATHEMATICS, APPLIED | HYPOELLIPTIC SDES DRIVEN | Holder continuous driving signal | INTEGRATION | FRACTIONAL BROWNIAN-MOTION | STATIONARY SOLUTIONS | SYSTEMS

Ordinary Differential Equations | Secondary: 34A34 | Differential equations | Primary: 37L15 | Mathematics | Applications of Mathematics | Exponential stability | Fractional Brownian motion | 34F05 | Partial Differential Equations | Hölder continuous driving signal | MATHEMATICS | ERGODICITY | MATHEMATICS, APPLIED | HYPOELLIPTIC SDES DRIVEN | Holder continuous driving signal | INTEGRATION | FRACTIONAL BROWNIAN-MOTION | STATIONARY SOLUTIONS | SYSTEMS

Journal Article

1995, ISBN 0023165405, xvi, 112

Book

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