Journal of the Royal Statistical Society. Series B, Statistical methodology, ISSN 1369-7412, 2007, Volume 69, Issue 5, pp. 741 - 796

We propose a new method for estimating parameters in models that are defined by a system of non-linear differential equations...

Approximation | Odes | Differential equations | Ordinary differential equations | Mathematical independent variables | Data smoothing | Parametric models | Modeling | Estimation methods | Dynamic modeling | Profiled estimation | Dynamic system | Differential equation | Parameter cascade | Estimating equation | Gauss | Newton method | Functional data analysis | Gauss-newton method | differential equation | gauss-newton method | MODELS | functional data analysis | SYSTEMS | STATISTICS & PROBABILITY | OPTIMIZATION | dynamic system | parameter cascade | estimating equation | profiled estimation | Nonlinear equations | Mathematics | Statistical analysis

Approximation | Odes | Differential equations | Ordinary differential equations | Mathematical independent variables | Data smoothing | Parametric models | Modeling | Estimation methods | Dynamic modeling | Profiled estimation | Dynamic system | Differential equation | Parameter cascade | Estimating equation | Gauss | Newton method | Functional data analysis | Gauss-newton method | differential equation | gauss-newton method | MODELS | functional data analysis | SYSTEMS | STATISTICS & PROBABILITY | OPTIMIZATION | dynamic system | parameter cascade | estimating equation | profiled estimation | Nonlinear equations | Mathematics | Statistical analysis

Journal Article

1991, Texts in applied mathematics, ISBN 0387972862, Volume 5, v. 1-2.

Book

International Journal of Modern Physics C, ISSN 0129-1831, 07/2018, Volume 29, Issue 7, p. 1850054

A representation formula for second-order nonhomogeneous nonlinear ordinary differential equations (ODEs...

traveling wave | Frasca's method | generalized separation of variables | generalized Burgers' equation | nonlinear Green's function | nonlinear wave equation with damping | nonlinear wave | method of lines | short tie expansion | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSTRUCTING FAMILIES | EXPANSION | SYSTEMS | Analysis | Differential equations

traveling wave | Frasca's method | generalized separation of variables | generalized Burgers' equation | nonlinear Green's function | nonlinear wave equation with damping | nonlinear wave | method of lines | short tie expansion | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | CONSTRUCTING FAMILIES | EXPANSION | SYSTEMS | Analysis | Differential equations

Journal Article

44.
Full Text
Exact Solutions for Some Fractional Partial Differential Equations by the (G′/G) Method

Mathematical problems in engineering, ISSN 1024-123X, 10/2013, Volume 2013, pp. 1 - 13

We apply the (G′/G) method to seek exact solutions for several fractional partial differential equations including the space-time fractional (2 + 1...

SOLITON-LIKE SOLUTIONS | (G'/G)-EXPANSION METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SERIES | ENGINEERING, MULTIDISCIPLINARY | FAMILIES | SYMBOLIC COMPUTATION | ADOMIAN DECOMPOSITION METHOD | RICCATI EQUATION | NONLINEAR EVOLUTION-EQUATIONS | PERIODIC-WAVE SOLUTIONS | Transformations (Mathematics) | Research | Variables (Mathematics) | Differential equations, Partial | Mathematical research | Transformations (mathematics) | Partial differential equations | Applied mathematics | Mathematical analysis | Spacetime | Exact solutions | Wave equations | Ordinary differential equations | Fractals | Control theory | Wave dispersion | Differential equations | Software | Transformations | Derivatives | Computer programs

SOLITON-LIKE SOLUTIONS | (G'/G)-EXPANSION METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SERIES | ENGINEERING, MULTIDISCIPLINARY | FAMILIES | SYMBOLIC COMPUTATION | ADOMIAN DECOMPOSITION METHOD | RICCATI EQUATION | NONLINEAR EVOLUTION-EQUATIONS | PERIODIC-WAVE SOLUTIONS | Transformations (Mathematics) | Research | Variables (Mathematics) | Differential equations, Partial | Mathematical research | Transformations (mathematics) | Partial differential equations | Applied mathematics | Mathematical analysis | Spacetime | Exact solutions | Wave equations | Ordinary differential equations | Fractals | Control theory | Wave dispersion | Differential equations | Software | Transformations | Derivatives | Computer programs

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 01/2019, Volume 95, Issue 1, pp. 361 - 368

The nonlinear space-time fractional differential equations (FDE) of Burgers' type play an important role for describing many phenomena in applied sciences...

Fractional partial differential equations | Kudryashov method | Burgers | CLASSIFICATION | MECHANICS | ENGINEERING, MECHANICAL | Methods | Differential equations | Ordinary differential equations | Traveling waves | Partial differential equations | Mathematical analysis

Fractional partial differential equations | Kudryashov method | Burgers | CLASSIFICATION | MECHANICS | ENGINEERING, MECHANICAL | Methods | Differential equations | Ordinary differential equations | Traveling waves | Partial differential equations | Mathematical analysis

Journal Article

Boundary value problems, ISSN 1687-2770, 2018, Volume 2018, Issue 1, pp. 1 - 15

.... Also, we study the existence of solutions for two such type high order fractional integro-differential equations...

Fractional integro-differential equation | Ordinary Differential Equations | Caputo–Fabrizio derivative | Analysis | 34A99 | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | High order derivation | Partial Differential Equations | 34A08 | MATHEMATICS | Caputo-Fabrizio derivative | MATHEMATICS, APPLIED | Mathematical analysis | Differential equations

Fractional integro-differential equation | Ordinary Differential Equations | Caputo–Fabrizio derivative | Analysis | 34A99 | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Mathematics | High order derivation | Partial Differential Equations | 34A08 | MATHEMATICS | Caputo-Fabrizio derivative | MATHEMATICS, APPLIED | Mathematical analysis | Differential equations

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 20

Existence and controllability results for nonlinear Hilfer fractional differential equations are studied...

34A37 | Approximate controllability | 26A33 | 34K37 | Mathematics | Impulsive condition | Ordinary Differential Equations | Functional Analysis | Analysis | 93B05 | Contraction mapping principle | Difference and Functional Equations | Mathematics, general | Controllability | Sobolev-type Hilfer fractional differential equation | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION | HADAMARD | Nonlinear equations | Partial differential equations | Mathematical analysis | Nonlinear control

34A37 | Approximate controllability | 26A33 | 34K37 | Mathematics | Impulsive condition | Ordinary Differential Equations | Functional Analysis | Analysis | 93B05 | Contraction mapping principle | Difference and Functional Equations | Mathematics, general | Controllability | Sobolev-type Hilfer fractional differential equation | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | EVOLUTION | HADAMARD | Nonlinear equations | Partial differential equations | Mathematical analysis | Nonlinear control

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 11/2016, Volume 306, pp. 179 - 199

In this paper, an explicit Runge–Kutta method for solving directly fourth-order ordinary differential equations (ODEs...

Relevant-colored trees | RKFD method | B-series | Fourth-order ordinary differential equations | NUMERICAL-METHODS | MATHEMATICS, APPLIED | LINEAR MULTISTEP METHOD | Methods | Differential equations | Trees | Construction | Illustrations | Converting | Computation | Mathematical models | Runge-Kutta method

Relevant-colored trees | RKFD method | B-series | Fourth-order ordinary differential equations | NUMERICAL-METHODS | MATHEMATICS, APPLIED | LINEAR MULTISTEP METHOD | Methods | Differential equations | Trees | Construction | Illustrations | Converting | Computation | Mathematical models | Runge-Kutta method

Journal Article

Journal of Dynamics and Differential Equations, ISSN 1040-7294, 12/2018, Volume 30, Issue 4, pp. 1921 - 1943

In this paper we prove that under mild conditions a nonautonomous Young differential equation possesses a unique solution which depends continuously on initial conditions...

Fractional Brownian motion (fBm) | Young integral | Ordinary Differential Equations | p -variation | Mathematics | Applications of Mathematics | Partial Differential Equations | Stochastic differential equations (SDE) | p-variation | MATHEMATICS, APPLIED | ROUGH SIGNALS | CALCULUS | FRACTIONAL BROWNIAN-MOTION | INEQUALITY | PATHS | DRIVEN | MATHEMATICS | INTEGRATION | Differential equations

Fractional Brownian motion (fBm) | Young integral | Ordinary Differential Equations | p -variation | Mathematics | Applications of Mathematics | Partial Differential Equations | Stochastic differential equations (SDE) | p-variation | MATHEMATICS, APPLIED | ROUGH SIGNALS | CALCULUS | FRACTIONAL BROWNIAN-MOTION | INEQUALITY | PATHS | DRIVEN | MATHEMATICS | INTEGRATION | Differential equations

Journal Article

1997, Australian Mathematical Society lecture series, ISBN 052144618X, Volume 10, x, 405

.... The authors concentrate on the techniques used to set up mathematical models and describe many systems in full detail, covering both differential and difference equations in depth...

Difference equations | Mathematical models | Differential equations

Difference equations | Mathematical models | Differential equations

Book

Advances in difference equations, ISSN 1687-1847, 2018, Volume 2018, Issue 1, pp. 1 - 7

In this article, the following boundary value problem of fractional differential equation with Riemann...

Mathematics | 35J05 | 34A08 | 34B18 | Ordinary Differential Equations | Fixed point theorem | Functional Analysis | Analysis | Mixed monotone operator | Riemann–Stieltjes integral | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | Existence and uniqueness | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Stieltjes integral | UNIQUENESS | Stieltjes integral | Operators (mathematics) | Fixed points (mathematics) | Boundary value problems | Existence theorems | Integrals | Differential equations | Boundary conditions | Derivatives

Mathematics | 35J05 | 34A08 | 34B18 | Ordinary Differential Equations | Fixed point theorem | Functional Analysis | Analysis | Mixed monotone operator | Riemann–Stieltjes integral | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | Existence and uniqueness | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Stieltjes integral | UNIQUENESS | Stieltjes integral | Operators (mathematics) | Fixed points (mathematics) | Boundary value problems | Existence theorems | Integrals | Differential equations | Boundary conditions | Derivatives

Journal Article

1991, Lecture notes in mathematics, ISBN 0387540849, Volume 1473, x, 317

In the theory of functional differential equations with infinite delay, there are several ways to choose the space of initial functions (phase space); and diverse (duplicated...

Delay differential equations | Global analysis (Mathematics) | Analysis

Delay differential equations | Global analysis (Mathematics) | Analysis

Book

2003, ISBN 0521016878, xi, 541

Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics...

Differential equations

Differential equations

Book

1995, Applied mathematical sciences, ISBN 0387944168, Volume 110, xi, 534

Book

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 10

We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations...

Ordinary Differential Equations | Functional Analysis | analytic approximation | Analysis | iterative reproducing kernel Hilbert space method | Difference and Functional Equations | Mathematics, general | Mathematics | inner product | Partial Differential Equations | fractional Riccati differential equation | MATHEMATICS | TIKHONOV REGULARIZATION | ORDER | MATHEMATICS, APPLIED | KERNEL HILBERT-SPACE | HOMOTOPY PERTURBATION METHOD | Usage | Hilbert space | Kernel functions | Iterative methods (Mathematics) | Differential equations | Tests, problems and exercises | Kernels | Reproduction | Difference equations | Mathematical analysis | Mathematical models | Calculus | Derivatives

Ordinary Differential Equations | Functional Analysis | analytic approximation | Analysis | iterative reproducing kernel Hilbert space method | Difference and Functional Equations | Mathematics, general | Mathematics | inner product | Partial Differential Equations | fractional Riccati differential equation | MATHEMATICS | TIKHONOV REGULARIZATION | ORDER | MATHEMATICS, APPLIED | KERNEL HILBERT-SPACE | HOMOTOPY PERTURBATION METHOD | Usage | Hilbert space | Kernel functions | Iterative methods (Mathematics) | Differential equations | Tests, problems and exercises | Kernels | Reproduction | Difference equations | Mathematical analysis | Mathematical models | Calculus | Derivatives

Journal Article

2005, Mathematical and analytical techniques with applications to engineering, ISBN 9780387252650, xvi, 352

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes...

Differential equations, Nonlinear | Differential equations, Partial | Mathematics | Engineering | Engineering Fluid Dynamics | Ordinary Differential Equations | Applications of Mathematics | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering

Differential equations, Nonlinear | Differential equations, Partial | Mathematics | Engineering | Engineering Fluid Dynamics | Ordinary Differential Equations | Applications of Mathematics | Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering

Book

Theoretical computer science, ISSN 0304-3975, 2015, Volume 599, pp. 64 - 78

In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE...

Ordinary differential equations | SBML | Chemical reaction network theory | Systems biology | PATHWAYS | CHEMICAL ORGANIZATION THEORY | MULTISTATIONARITY | TEMPORAL LOGIC | REPRESENTATION | REACTION NETWORKS | MODELS | REGULATORY NETWORKS | BIOLOGY | COMPUTER SCIENCE, THEORY & METHODS | CYCLE | Public software | Algorithms | Chemical reaction, Rate of | Analysis | Differential equations | Computer simulation | Dynamics | Reaction kinetics | Mathematical models | Biochemistry | Statistics | Dynamical systems | Bioinformatics | Computer Science

Ordinary differential equations | SBML | Chemical reaction network theory | Systems biology | PATHWAYS | CHEMICAL ORGANIZATION THEORY | MULTISTATIONARITY | TEMPORAL LOGIC | REPRESENTATION | REACTION NETWORKS | MODELS | REGULATORY NETWORKS | BIOLOGY | COMPUTER SCIENCE, THEORY & METHODS | CYCLE | Public software | Algorithms | Chemical reaction, Rate of | Analysis | Differential equations | Computer simulation | Dynamics | Reaction kinetics | Mathematical models | Biochemistry | Statistics | Dynamical systems | Bioinformatics | Computer Science

Journal Article