Journal of mathematical analysis and applications, ISSN 0022-247X, 2010, Volume 367, Issue 1, pp. 260 - 272

...–Liouville sequential fractional derivative by using monotone iterative method.

Fractional differential equation | Riemann–Liouville sequential fractional derivatives | Initial value problem | Upper solution and lower solution | Riemann-Liouville sequential fractional derivatives | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | INTEGRAL-EQUATIONS | UNIQUENESS | MATHEMATICS | ORDER | MONOTONE ITERATIVE TECHNIQUE | 1ST-ORDER

Fractional differential equation | Riemann–Liouville sequential fractional derivatives | Initial value problem | Upper solution and lower solution | Riemann-Liouville sequential fractional derivatives | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | INTEGRAL-EQUATIONS | UNIQUENESS | MATHEMATICS | ORDER | MONOTONE ITERATIVE TECHNIQUE | 1ST-ORDER

Journal Article

Journal of mathematical analysis and applications, ISSN 0022-247X, 2011, Volume 384, Issue 2, pp. 211 - 231

...–Liouville sequential fractional derivative by using monotone iterative method. An example is presented to illustrate our main result.

Impulsive | Periodic boundary value problem | Riemann–Liouville sequential fractional derivative | Riemann-Liouville sequential fractional derivative | EXISTENCE | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | INITIAL-VALUE PROBLEMS | UNIQUENESS

Impulsive | Periodic boundary value problem | Riemann–Liouville sequential fractional derivative | Riemann-Liouville sequential fractional derivative | EXISTENCE | SPACE | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | INITIAL-VALUE PROBLEMS | UNIQUENESS

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2008, Volume 53, Issue 1, pp. 67 - 74

.... In this study, the fractional discrete Lagrangians which differs by a fractional derivative are analyzed within Riemann...

Automotive and Aerospace Engineering, Traffic | Fractional Riemann–Liouville derivative | Faà di Bruno formula | Engineering | Vibration, Dynamical Systems, Control | Fractional Euler–Lagrange equations | Mechanics | Fractional Lagrangians | Mechanical Engineering | Fractional calculus | Fractional Euler-Lagrange equations | Fractional Riemann-Liouville derivative | CLASSICAL FIELDS | fractional calculus | SEQUENTIAL MECHANICS | Faa di Bruno formula | CALCULUS | fractional Lagrangians | FORMULATION | ENGINEERING, MECHANICAL | fractional Riemann-Liouville derivative | fractional Euler-Lagrange equations | MECHANICS | LINEAR VELOCITIES | SYSTEMS | VARIATIONAL-PROBLEMS | FORMALISM | Mechanics (physics) | Mathematical analysis | Classical mechanics | Euler-Lagrange equation | Equations of motion | Variational principles

Automotive and Aerospace Engineering, Traffic | Fractional Riemann–Liouville derivative | Faà di Bruno formula | Engineering | Vibration, Dynamical Systems, Control | Fractional Euler–Lagrange equations | Mechanics | Fractional Lagrangians | Mechanical Engineering | Fractional calculus | Fractional Euler-Lagrange equations | Fractional Riemann-Liouville derivative | CLASSICAL FIELDS | fractional calculus | SEQUENTIAL MECHANICS | Faa di Bruno formula | CALCULUS | fractional Lagrangians | FORMULATION | ENGINEERING, MECHANICAL | fractional Riemann-Liouville derivative | fractional Euler-Lagrange equations | MECHANICS | LINEAR VELOCITIES | SYSTEMS | VARIATIONAL-PROBLEMS | FORMALISM | Mechanics (physics) | Mathematical analysis | Classical mechanics | Euler-Lagrange equation | Equations of motion | Variational principles

Journal Article

Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 22

.... We first provide some properties of Hilfer fractional derivative, and then establish Lyapunov-type inequalities for a sequential Hilfer fractional differential equation with two types of multi-point boundary conditions...

Multi-point boundary condition | 34B15 | Hilfer fractional derivative | Analysis | Sequential fractional differential equation | Mathematics, general | Mathematics | Applications of Mathematics | 34A08 | Lyapunov-type inequality | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | Boundary conditions | Boundary value problems | Inequalities | Differential equations

Multi-point boundary condition | 34B15 | Hilfer fractional derivative | Analysis | Sequential fractional differential equation | Mathematics, general | Mathematics | Applications of Mathematics | 34A08 | Lyapunov-type inequality | MATHEMATICS | MATHEMATICS, APPLIED | DIFFERENTIAL-EQUATIONS | Boundary conditions | Boundary value problems | Inequalities | Differential equations

Journal Article

Applied mathematics and computation, ISSN 0096-3003, 2007, Volume 187, Issue 2, pp. 777 - 784

In this paper, we further discuss the properties of three kinds of fractional derivatives...

Riemann–Liouville derivative | Caputo derivative | Grünwald–Letnikov derivative | Consistency | Sequential property | Riemann-Liouville derivative | Grünwald-Letnikov derivative | sequential property | SYSTEM | ORDER | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | CHAOS SYNCHRONIZATION | DIFFERENTIAL-EQUATIONS | Grunwald-Letnikov derivative | Derivatives (Financial instruments)

Riemann–Liouville derivative | Caputo derivative | Grünwald–Letnikov derivative | Consistency | Sequential property | Riemann-Liouville derivative | Grünwald-Letnikov derivative | sequential property | SYSTEM | ORDER | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | CHAOS SYNCHRONIZATION | DIFFERENTIAL-EQUATIONS | Grunwald-Letnikov derivative | Derivatives (Financial instruments)

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2005, Volume 304, Issue 2, pp. 599 - 606

The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied...

Nonconservative systems | Hamiltonian system | Fractional derivative | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENTIAL MECHANICS | nonconservative systems | EQUATIONS | fractional derivative | VARIATIONAL-PROBLEMS

Nonconservative systems | Hamiltonian system | Fractional derivative | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENTIAL MECHANICS | nonconservative systems | EQUATIONS | fractional derivative | VARIATIONAL-PROBLEMS

Journal Article

中国物理B：英文版, ISSN 1674-1056, 2012, Volume 21, Issue 8, pp. 302 - 306

.... A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established...

衍生 | 运动微分方程 | 分数阶微分方程 | 工具 | 哈密顿正则方程 | 黎曼 | 哈密顿原理 | 拉格朗日方程 | fractional Hamilton canonical equation | fractional Hamilton principle | combined Riemann-Liouville fractional derivative | fractional Lagrange equation | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION | HAMILTON FORMALISM | EULER-LAGRANGE | Operators (mathematics) | Mathematical analysis | Hamilton's principle | Differential equations | Paper | Derivatives | Variational principles | Mechanical systems

衍生 | 运动微分方程 | 分数阶微分方程 | 工具 | 哈密顿正则方程 | 黎曼 | 哈密顿原理 | 拉格朗日方程 | fractional Hamilton canonical equation | fractional Hamilton principle | combined Riemann-Liouville fractional derivative | fractional Lagrange equation | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION | HAMILTON FORMALISM | EULER-LAGRANGE | Operators (mathematics) | Mathematical analysis | Hamilton's principle | Differential equations | Paper | Derivatives | Variational principles | Mechanical systems

Journal Article

Czechoslovak Journal of Physics, ISSN 1572-9486, 2006, Volume 56, Issue 10, pp. 1087 - 1092

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives...

fractional Hamiltonian formulation | fractional Euler-Lagrange equations | Physics, general | Nuclear Physics, Heavy Ions, Hadrons | Caputo derivative | Physics | Fractional Hamiltonian formulation | Fractional Euler-Lagrange equations | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION

fractional Hamiltonian formulation | fractional Euler-Lagrange equations | Physics, general | Nuclear Physics, Heavy Ions, Hadrons | Caputo derivative | Physics | Fractional Hamiltonian formulation | Fractional Euler-Lagrange equations | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | EQUATIONS | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION

Journal Article

Advances in difference equations, ISSN 1687-1847, 2019, Volume 2019, Issue 1, pp. 1 - 25

We investigate the existence of solutions for new boundary value problems of Caputo-type sequential fractional differential equations and inclusions supplemented with nonlocal integro-multipoint boundary conditions...

34B15 | Sequential fractional derivative | 34B10 | Mathematics | Inclusions | 34A08 | Integro-multipoint boundary conditions | Ordinary Differential Equations | Functional Analysis | Nonlocal | Analysis | Difference and Functional Equations | Mathematics, general | 34A60 | Partial Differential Equations | Existence | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | Boundary conditions | Boundary value problems | Functional analysis | Differential equations

34B15 | Sequential fractional derivative | 34B10 | Mathematics | Inclusions | 34A08 | Integro-multipoint boundary conditions | Ordinary Differential Equations | Functional Analysis | Nonlocal | Analysis | Difference and Functional Equations | Mathematics, general | 34A60 | Partial Differential Equations | Existence | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | POSITIVE SOLUTIONS | DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | Boundary conditions | Boundary value problems | Functional analysis | Differential equations

Journal Article

Nonlinear dynamics, ISSN 1573-269X, 2007, Volume 53, Issue 3, pp. 215 - 222

Using the recent formulation of Noether’s theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler...

Automotive and Aerospace Engineering, Traffic | Noether’s theorem | Conservation laws | Engineering | Vibration, Dynamical Systems, Control | Optimal control | Mechanics | Mechanical Engineering | Fractional derivatives | Symmetry | Noether's theorem | SEQUENTIAL MECHANICS | CALCULUS | EQUATIONS | optimal control | ENGINEERING, MECHANICAL | ORDER | fractional derivatives | MECHANICS | conservation laws | symmetry | LINEAR VELOCITIES | SYSTEMS | HAMILTONIAN-FORMULATION | VARIATIONAL-PROBLEMS | FORMALISM | DERIVATIVES | Environmental law | Economic models | Theorems | Lagrange multiplier | Lagrange multipliers | Legislation | Control theory | Euler-Lagrange equation | Calculus of variations | State variable

Automotive and Aerospace Engineering, Traffic | Noether’s theorem | Conservation laws | Engineering | Vibration, Dynamical Systems, Control | Optimal control | Mechanics | Mechanical Engineering | Fractional derivatives | Symmetry | Noether's theorem | SEQUENTIAL MECHANICS | CALCULUS | EQUATIONS | optimal control | ENGINEERING, MECHANICAL | ORDER | fractional derivatives | MECHANICS | conservation laws | symmetry | LINEAR VELOCITIES | SYSTEMS | HAMILTONIAN-FORMULATION | VARIATIONAL-PROBLEMS | FORMALISM | DERIVATIVES | Environmental law | Economic models | Theorems | Lagrange multiplier | Lagrange multipliers | Legislation | Control theory | Euler-Lagrange equation | Calculus of variations | State variable

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2015, Volume 2015, Issue 1, pp. 1 - 13

This paper deals with the following initial value problem for nonlinear fractional differential equation with sequential fractional derivative: { D 0 α 2 c...

34A12 | 26A33 | Mathematics | existence and uniqueness | Caputo fractional derivative | 34A08 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | sequential fractional derivative | Partial Differential Equations | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Fixed point theory | Usage | Differential equations | Theorems | Difference equations | Uniqueness | Texts | Nonlinearity | Initial value problems | Derivatives

34A12 | 26A33 | Mathematics | existence and uniqueness | Caputo fractional derivative | 34A08 | Ordinary Differential Equations | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | sequential fractional derivative | Partial Differential Equations | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | Fixed point theory | Usage | Differential equations | Theorems | Difference equations | Uniqueness | Texts | Nonlinearity | Initial value problems | Derivatives

Journal Article

International Journal of Non-Linear Mechanics, ISSN 0020-7462, 04/2017, Volume 90, pp. 32 - 38

Based on Riemann-Liouville fractional derivatives, conserved quantities and adiabatic invariants for fractional generalized Birkhoffian systems are investigated...

Conserved quantity | Riemann-Liouville fractional derivative | Adiabatic invariant | Generalized Birkhoffian system | SEQUENTIAL MECHANICS | CALCULUS | PERTURBATION | LAGRANGIANS | MEI SYMMETRY | FORMULATION | MECHANICS | DYNAMICAL-SYSTEMS | NOETHERS THEOREM | Generalized Birlchoffian system | VARIATIONAL-PROBLEMS | DERIVATIVES

Conserved quantity | Riemann-Liouville fractional derivative | Adiabatic invariant | Generalized Birkhoffian system | SEQUENTIAL MECHANICS | CALCULUS | PERTURBATION | LAGRANGIANS | MEI SYMMETRY | FORMULATION | MECHANICS | DYNAMICAL-SYSTEMS | NOETHERS THEOREM | Generalized Birlchoffian system | VARIATIONAL-PROBLEMS | DERIVATIVES

Journal Article

Physica Scripta, ISSN 1402-4896, 01/2008, Volume 77, Issue 1, p. 015101

A new fractional Hamilton-Jacobi formulation for discrete systems in terms of fractional Caputo derivatives was developed...

NUMERICAL SCHEME | CLASSICAL FIELDS | ORDER | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | DIFFERENTIAL-EQUATIONS | DIFFUSION | QUANTUM-MECHANICS | EULER-LAGRANGE EQUATIONS | OSCILLATOR

NUMERICAL SCHEME | CLASSICAL FIELDS | ORDER | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | DIFFERENTIAL-EQUATIONS | DIFFUSION | QUANTUM-MECHANICS | EULER-LAGRANGE EQUATIONS | OSCILLATOR

Journal Article

Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2008, Volume 41, Issue 31, p. 315403

The fractional variational principles within Riemann-Liouville fractional derivatives in the presence of delay are analyzed...

NUMERICAL SCHEME | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | LINEAR VELOCITIES | DIFFERENTIAL-EQUATIONS | HAMILTONIAN-FORMULATION | FORMALISM | PHYSICS, MATHEMATICAL | EULER-LAGRANGE EQUATIONS | DERIVATIVES

NUMERICAL SCHEME | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | LINEAR VELOCITIES | DIFFERENTIAL-EQUATIONS | HAMILTONIAN-FORMULATION | FORMALISM | PHYSICS, MATHEMATICAL | EULER-LAGRANGE EQUATIONS | DERIVATIVES

Journal Article

15.
Full Text
Nonlinear sequential fractional differential equations with nonlocal boundary conditions

Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 15

This article develops the existence theory for sequential fractional differential equations involving Caputo fractional derivative of order 1 < α < 2 $1<\alpha<2...

34B10 | existence | Mathematics | Caputo fractional derivative | 34A08 | Ordinary Differential Equations | Functional Analysis | fixed point | Analysis | Difference and Functional Equations | Mathematics, general | sequential fractional derivative | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Fixed point theory | Theorems (Mathematics) | Boundary value problems | Usage | Differential equations | Boundary conditions | Nonlinear equations | Derivatives | Mathematical analysis | Integrals

34B10 | existence | Mathematics | Caputo fractional derivative | 34A08 | Ordinary Differential Equations | Functional Analysis | fixed point | Analysis | Difference and Functional Equations | Mathematics, general | sequential fractional derivative | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | Fixed point theory | Theorems (Mathematics) | Boundary value problems | Usage | Differential equations | Boundary conditions | Nonlinear equations | Derivatives | Mathematical analysis | Integrals

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 6/2008, Volume 52, Issue 4, pp. 331 - 335

In this paper, first a class of fractional differential equations are obtained by using the fractional variational principles...

Automotive and Aerospace Engineering, Traffic | Engineering | Vibration, Dynamical Systems, Control | Mechanics | Fractional variational calculus | Mechanical Engineering | Differential equations of fractional order | Fractional calculus | fractional variational calculus | FIELDS | fractional calculus | MECHANICS | SEQUENTIAL MECHANICS | differential equations of fractional order | LINEAR VELOCITIES | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION | DERIVATIVES | ENGINEERING, MECHANICAL | Euler-Lagrange equation | Variational principles | Mathematical analysis | Exact solutions | Differential equations

Automotive and Aerospace Engineering, Traffic | Engineering | Vibration, Dynamical Systems, Control | Mechanics | Fractional variational calculus | Mechanical Engineering | Differential equations of fractional order | Fractional calculus | fractional variational calculus | FIELDS | fractional calculus | MECHANICS | SEQUENTIAL MECHANICS | differential equations of fractional order | LINEAR VELOCITIES | SYSTEMS | VARIATIONAL-PROBLEMS | FORMULATION | DERIVATIVES | ENGINEERING, MECHANICAL | Euler-Lagrange equation | Variational principles | Mathematical analysis | Exact solutions | Differential equations

Journal Article

International journal of nonlinear sciences and numerical simulation, ISSN 2191-0294, 2018, Volume 19, Issue 7-8, pp. 763 - 774

This paper deals with a new class of non-linear impulsive sequential fractional differential equations with multi-point boundary conditions using Caputo fractional derivative, where impulses are non instantaneous...

34B27 | non-instantaneous impulses | 26A33 | sequential fractional differential equation | fractional integral | Ulam’s type stability | Caputo fractional derivative | fixed point theorem | 34A08 | Ulam's type stability | noninstantaneous impulses | HYERS-ULAM STABILITY | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | ORDER | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SYSTEMS | Impulses | Boundary conditions | Boundary value problems | Stability analysis | Mathematical analysis | Differential equations

34B27 | non-instantaneous impulses | 26A33 | sequential fractional differential equation | fractional integral | Ulam’s type stability | Caputo fractional derivative | fixed point theorem | 34A08 | Ulam's type stability | noninstantaneous impulses | HYERS-ULAM STABILITY | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | INITIAL-VALUE PROBLEMS | ORDER | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | SYSTEMS | Impulses | Boundary conditions | Boundary value problems | Stability analysis | Mathematical analysis | Differential equations

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 344, Issue 2, pp. 799 - 805

As a continuation of Rabei et al. work [Eqab M. Rabei, Khaled I. Nawafleh, Raed S. Hijjawi, Sami I. Muslih, Dumitru Baleanu, The Hamilton formalism with fractional derivatives, J...

Hamiltonian formalisms | Fractional systems | Hamilton–Jacobi treatment | Fractional derivative | Hamilton-Jacobi treatment | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENTIAL MECHANICS | fractional systems | fractional derivative | DERIVATIVES

Hamiltonian formalisms | Fractional systems | Hamilton–Jacobi treatment | Fractional derivative | Hamilton-Jacobi treatment | MATHEMATICS | MATHEMATICS, APPLIED | SEQUENTIAL MECHANICS | fractional systems | fractional derivative | DERIVATIVES

Journal Article

International Journal of Theoretical Physics, ISSN 0020-7748, 4/2009, Volume 48, Issue 4, pp. 1044 - 1052

The fractional generalization of Nambu mechanics is constructed by using the differential forms and exterior derivatives of fractional orders...

Nambu mechanics | Mathematical and Computational Physics | Hamiltonian mechanics | Quantum Physics | Physics, general | Fractional differential forms | Physics | Elementary Particles, Quantum Field Theory | Fractional derivative | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | HAMILTONIAN-MECHANICS | FORMULATION | DYNAMICS | SYSTEMS | FORMALISM | DERIVATIVES | EQUATION

Nambu mechanics | Mathematical and Computational Physics | Hamiltonian mechanics | Quantum Physics | Physics, general | Fractional differential forms | Physics | Elementary Particles, Quantum Field Theory | Fractional derivative | SEQUENTIAL MECHANICS | PHYSICS, MULTIDISCIPLINARY | HAMILTONIAN-MECHANICS | FORMULATION | DYNAMICS | SYSTEMS | FORMALISM | DERIVATIVES | EQUATION

Journal Article