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Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2016, Volume 299, pp. 159 - 175
In this paper, a series of new high-order numerical approximations to th order Caputo derivative is constructed by using th degree interpolation approximation... 
Difference scheme | Advection–diffusion equation | Caputo derivative | Convergence | Advection-diffusion equation | MATHEMATICS, APPLIED | Approximation | Mathematical analysis | Dirichlet problem | Truncation errors | Mathematical models | Derivatives
Journal Article
2008, ISBN 9781587296314, xxii, 217
Book
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 07/2017, Volume 48, pp. 520 - 530
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 06/2015, Volume 18, Issue 3, pp. 735 - 761
In this paper, we first establish a high-order numerical algorithm for α-th (0 < α < 1) order Caputo derivative of a given function f(t), where the convergence... 
convergence | difference scheme | Caputo derivative | stability | advection-diffusion equation | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | FRACTIONAL SUBDIFFUSION EQUATION | Usage | Approximation theory | Heat equation | Analysis
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 07/2017, Volume 38, Issue 7, pp. 861 - 890
In this paper, a series of new high-order numerical approximations to α-th Caputo derivatives (0<α<2) is derived based on a compound of shift operators and... 
Fourier transform | high-order approximation | Caputo-type advection-diffusion equation | convergence | Caputo derivative | 26A33 | MATHEMATICS, APPLIED | Operators (mathematics) | Advection-diffusion equation | Advection | Derivatives | Mathematical analysis
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 12/2017, Volume 315, pp. 549 - 554
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2015, Volume 438, pp. 335 - 339
A fractional difference is defined by the use of the right and the left Caputo fractional differences. The definition is a two-sided operator of Riesz type and... 
Discrete fractional calculus | Riesz–Caputo difference | Fractional partial difference equations | Riesz-Caputo difference | CHAOS | PHYSICS, MULTIDISCIPLINARY | DISPERSION | CALCULUS | SYSTEMS
Journal Article
Journal Article
International Journal of Robust and Nonlinear Control, ISSN 1049-8923, 08/2019, Volume 29, Issue 12, pp. 4041 - 4055
Journal Article
The European Physical Journal Special Topics, ISSN 1951-6355, 12/2017, Volume 226, Issue 16, pp. 3411 - 3425
This paper is concerned with a class of boundary value problems for fractional differential equations with the Riesz–Caputo derivative, which holds two-sided... 
Condensed Matter Physics | Measurement Science and Instrumentation | Materials Science, general | Classical and Continuum Physics | Atomic, Molecular, Optical and Plasma Physics | Physics, general | Physics | ULAM-HYERS STABILITY | SYSTEMS | PHYSICS, MULTIDISCIPLINARY | TERMS | Information science | Differential equations | Resveratrol
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 09/2017, Volume 102, pp. 305 - 318
Journal Article
Applied Numerical Mathematics, ISSN 0168-9274, 10/2018, Volume 132, pp. 138 - 153
In this paper, we study the recently introduced Caputo and Fabrizio operator, which this new operator was derived by replacing the singular kernel in the... 
Shifted Legendre operational matrix | Fractional differential equations | Caputo–Fabrizio operator | Caputo fractional derivative | MATHEMATICS, APPLIED | Caputo-Fabrizio operator | Differential equations
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 09/2017, Volume 102, pp. 99 - 105
This paper investigates chaotic behavior and stability of fractional differential equations within a new generalized Caputo derivative. A semi–analytical... 
Chaos | Asymptotic stability | Generalized Caputo derivative | Adomian decomposition method | Numerical solutions | Lyapunov direct method | SYSTEM | MATRIX | PHYSICS, MULTIDISCIPLINARY | ALGORITHM | PHYSICS, MATHEMATICAL | SPECTRAL METHOD | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DYNAMICS | DIFFUSION | Information science | Analysis | Differential equations
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 9/2019, Volume 97, Issue 4, pp. 2521 - 2531
A lemma widely used for Lyapunov stability analysis of Caputo fractional-order systems (CFOSs): let $$x(t)\in {\mathbb {R}}^n$$ x ( t ) ∈ R n be a vector of... 
Engineering | Vibration, Dynamical Systems, Control | Quadratic Lyapunov function | Estimation | Classical Mechanics | Lyapunov stability | Derivative | Automotive Engineering | Mechanical Engineering | Caputo fractional-order system | MECHANICS | ENGINEERING, MECHANICAL | Information science | Analysis | Nuclear physics
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 08/2018, Volume 61, pp. 138 - 148
Journal Article
Discrete Dynamics in Nature and Society, ISSN 1026-0226, 2011, Volume 2011, pp. 1 - 15
Recently, many models are formulated in terms of fractional derivatives, such as in control processing, viscoelasticity, signal processing, and anomalous... 
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | BROWNIAN MOTIONS | DYNAMICS DRIVEN | MULTIDISCIPLINARY SCIENCES | DIFFUSION | FRACTIONAL DIFFERENTIAL-EQUATIONS | STOCHASTIC-SYSTEMS | Analysis | Calculus | Studies | Derivatives | Viscoelasticity | Dynamics | Mathematical analysis | Signal processing | Mathematical models | Diffusion
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2019, Volume 42, Issue 1, pp. 175 - 185
Journal Article