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

Journal Article

Advances in Difference Equations, 12/2018, Volume 2018, Issue 1, pp. 1 - 11

We extend the fractional Caputo–Fabrizio derivative of order 0≤σ<1 $0\leq \sigma <1$ on CR[0,1] $C_{\mathbb{R}}[0,1]$ and investigate two higher-order...

Ordinary Differential Equations | Functional Analysis | Analysis | 34A99 | Difference and Functional Equations | The extended Caputo–Fabrizio derivative of order 0 ≤ σ < 1 $0\leq \sigma <1 | Series-type equation | Mathematics, general | Higher-order fractional differential equation | Mathematics | Partial Differential Equations | 34A08

Ordinary Differential Equations | Functional Analysis | Analysis | 34A99 | Difference and Functional Equations | The extended Caputo–Fabrizio derivative of order 0 ≤ σ < 1 $0\leq \sigma <1 | Series-type equation | Mathematics, general | Higher-order fractional differential equation | Mathematics | Partial Differential Equations | 34A08

Journal Article

Advances in Difference Equations, ISSN 1687-1847, 12/2018, Volume 2018, Issue 1

Journal Article

ADVANCES IN DIFFERENCE EQUATIONS, ISSN 1687-1847, 07/2018

We extend the fractional Caputo-Fabrizio derivative of order 0 <= sigma < 1 on C-R[0,1] and investigate two higher-order series-type fractional differential...

MATHEMATICS | MATHEMATICS, APPLIED | Series-type equation | The extended Caputo-Fabrizio derivative of order 0 <= sigma < 1 | Higher-order fractional differential equation | DIFFUSION

MATHEMATICS | MATHEMATICS, APPLIED | Series-type equation | The extended Caputo-Fabrizio derivative of order 0 <= sigma < 1 | Higher-order fractional differential equation | DIFFUSION

Journal Article

The European Physical Journal Plus, ISSN 2190-5444, 3/2018, Volume 133, Issue 3, pp. 1 - 12

In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal...

Condensed Matter Physics | Atomic, Molecular, Optical and Plasma Physics | Applied and Technical Physics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MODEL | PHYSICS, MULTIDISCIPLINARY | EQUATION | HOMOTOPY ANALYSIS METHOD

Condensed Matter Physics | Atomic, Molecular, Optical and Plasma Physics | Applied and Technical Physics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | MODEL | PHYSICS, MULTIDISCIPLINARY | EQUATION | HOMOTOPY ANALYSIS METHOD

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2019, Volume 346, pp. 247 - 260

In this paper, we present a new definition of fractional-order derivative with a smooth kernel based on the Caputo–Fabrizio fractional-order operator which...

Modified-Caputo–Fabrizio derivative | Multi step homotopy analysis method | Fractional calculus | Homotopy analysis method | SPACE | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | Modified-Caputo-Fabrizio derivative | TRANSFORM METHOD | SYSTEMS | Methods | Differential equations

Modified-Caputo–Fabrizio derivative | Multi step homotopy analysis method | Fractional calculus | Homotopy analysis method | SPACE | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | Modified-Caputo-Fabrizio derivative | TRANSFORM METHOD | SYSTEMS | Methods | Differential equations

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 18

A Caputo–Fabrizio type fractional order mathematical model for the dynamics of pine wilt disease (FPWD) is presented. The basic properties of the model are...

Pint wilt disease | Ordinary Differential Equations | Fixed point theorem | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Caputo–Fabrizio (CF) fractional derivative | Numerical simulation | Mathematics | Mathematical model | Partial Differential Equations | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSMISSION | NEMATODA-APHELENCHOIDIDAE | MATHEMATICAL-ANALYSIS | NETWORKS | Caputo-Fabrizio (CF) fractional derivative | Fixed points (mathematics) | Order parameters | Mathematical models | Computer simulation

Pint wilt disease | Ordinary Differential Equations | Fixed point theorem | Functional Analysis | Analysis | Difference and Functional Equations | Mathematics, general | Caputo–Fabrizio (CF) fractional derivative | Numerical simulation | Mathematics | Mathematical model | Partial Differential Equations | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | TRANSMISSION | NEMATODA-APHELENCHOIDIDAE | MATHEMATICAL-ANALYSIS | NETWORKS | Caputo-Fabrizio (CF) fractional derivative | Fixed points (mathematics) | Order parameters | Mathematical models | Computer simulation

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 08/2018, Volume 61, pp. 138 - 148

The Gaussian function has been employed in a vast number of practical and theoretical applications since it was proposed. Likewise, Gaussian function and its...

Gaussian-based derivatives | Caputo–Fabrizio analytic solution | Fractional-order signal processing | Fractional calculus | RESISTING MEDIUM | MATHEMATICS, APPLIED | FILTER | PHYSICS, FLUIDS & PLASMAS | CALCULUS | Caputo-Fabrizio analytic solution | ALGORITHMS | MODEL | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MOTION | IMAGES | FAULT-DIAGNOSIS

Gaussian-based derivatives | Caputo–Fabrizio analytic solution | Fractional-order signal processing | Fractional calculus | RESISTING MEDIUM | MATHEMATICS, APPLIED | FILTER | PHYSICS, FLUIDS & PLASMAS | CALCULUS | Caputo-Fabrizio analytic solution | ALGORITHMS | MODEL | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MOTION | IMAGES | FAULT-DIAGNOSIS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 01/2017, Volume 73, Issue 1, pp. 1 - 10

The advection–diffusion equation with time-fractional derivatives without singular kernel and two space-variables is considered. The fundamental solutions in a...

Fundamental solutions | Dirichlet problem | Caputo–Fabrizio derivative | Advection–diffusion equation | Advection-diffusion equation | Caputo-Fabrizio derivative | MATHEMATICS, APPLIED | Kernels | Fourier transforms | Mathematical analysis | Mathematical models | Derivatives | Laplace transforms | Diffusion

Fundamental solutions | Dirichlet problem | Caputo–Fabrizio derivative | Advection–diffusion equation | Advection-diffusion equation | Caputo-Fabrizio derivative | MATHEMATICS, APPLIED | Kernels | Fourier transforms | Mathematical analysis | Mathematical models | Derivatives | Laplace transforms | Diffusion

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2017, Volume 74, Issue 10, pp. 2503 - 2519

Unsteady flows of an incompressible Maxwell fluid with Caputo–Fabrizio time-fractional derivatives through a circular tube are studied. Flows are generated by...

Electrokinetic flow | Micro-tubes | Caputo–Fabrizio fractional derivatives | Joule heating effect | Maxwell fluid | DISSIPATION | MATHEMATICS, APPLIED | DESIGN | HEAT-TRANSFER | Caputo-Fabrizio fractional derivatives | ON-A-CHIP | ELECTROMAGNETOHYDRODYNAMIC FLOW | TRANSPORT | MAGNETIC-FIELD | FREE-CONVECTION FLOW | MICROFLUIDICS | BLOOD | Magnetic fields | Electric fields | Analysis | Derivatives (Financial instruments)

Electrokinetic flow | Micro-tubes | Caputo–Fabrizio fractional derivatives | Joule heating effect | Maxwell fluid | DISSIPATION | MATHEMATICS, APPLIED | DESIGN | HEAT-TRANSFER | Caputo-Fabrizio fractional derivatives | ON-A-CHIP | ELECTROMAGNETOHYDRODYNAMIC FLOW | TRANSPORT | MAGNETIC-FIELD | FREE-CONVECTION FLOW | MICROFLUIDICS | BLOOD | Magnetic fields | Electric fields | Analysis | Derivatives (Financial instruments)

Journal Article

Applied Mathematical Modelling, ISSN 0307-904X, 04/2019, Volume 68, pp. 603 - 615

In this study, the non-Darcian flow and solute transport in porous media are modeled with a revised Caputo derivative called the Caputo–Fabrizio fractional...

Caputo–Fabrizio fractional derivative | Non-Darcian flow | Swartzendruber model | Diffusive transport | DISSIPATION | CONCRETE | Caputo-Fabrizio fractional derivative | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FLUID | SHALE | DYNAMICS | DIFFUSION | FRACTIONAL DERIVATIVES | WATER | Porous media | Soil water | Soil mixtures | Sensitivity analysis | Transport | Diffusion

Caputo–Fabrizio fractional derivative | Non-Darcian flow | Swartzendruber model | Diffusive transport | DISSIPATION | CONCRETE | Caputo-Fabrizio fractional derivative | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | FLUID | SHALE | DYNAMICS | DIFFUSION | FRACTIONAL DERIVATIVES | WATER | Porous media | Soil water | Soil mixtures | Sensitivity analysis | Transport | Diffusion

Journal Article

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Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales

Nonlinear Analysis: Hybrid Systems, ISSN 1751-570X, 05/2019, Volume 32, pp. 168 - 176

Caputo–Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the...

Existence and uniqueness of solution | Calculus on time scales | Exponential stability | Laplace transform on time scales | Caputo–Fabrizio fractional delta derivatives and integral | EXISTENCE | MATHEMATICS, APPLIED | CALCULUS | Caputo-Fabrizio fractional delta derivatives and integral | AUTOMATION & CONTROL SYSTEMS | Linear systems | Calculus | Laplace transformation | Research | Mathematical research | Mathematics - Classical Analysis and ODEs

Existence and uniqueness of solution | Calculus on time scales | Exponential stability | Laplace transform on time scales | Caputo–Fabrizio fractional delta derivatives and integral | EXISTENCE | MATHEMATICS, APPLIED | CALCULUS | Caputo-Fabrizio fractional delta derivatives and integral | AUTOMATION & CONTROL SYSTEMS | Linear systems | Calculus | Laplace transformation | Research | Mathematical research | Mathematics - Classical Analysis and ODEs

Journal Article

Mechanics of Time-Dependent Materials, ISSN 1385-2000, 5/2019, Volume 23, Issue 2, pp. 133 - 151

This paper presents a study of Walters’-B fluid with Caputo–Fabrizio fractional derivatives through an infinitely long oscillating vertical plate by Newtonian...

Polymer Sciences | Stehfest’s algorithm | Caputo–Fabrizio derivatives | Engineering | Walter’s-B fluid | Solid Mechanics | Classical Mechanics | Characterization and Evaluation of Materials | Newtonian heating | Magnetic field | Algorithms | Magnetic fields | Analysis | Differential equations

Polymer Sciences | Stehfest’s algorithm | Caputo–Fabrizio derivatives | Engineering | Walter’s-B fluid | Solid Mechanics | Classical Mechanics | Characterization and Evaluation of Materials | Newtonian heating | Magnetic field | Algorithms | Magnetic fields | Analysis | Differential equations

Journal Article

BOUNDARY VALUE PROBLEMS, ISSN 1687-2770, 04/2019, Volume 2019, Issue 1, pp. 1 - 17

We first show that four fractional integro-differential inclusions have solutions. Also, we show that dimension of the set of solutions for the second...

MATHEMATICS | MATHEMATICS, APPLIED | Dimension of the set of solutions | Fractional differential inclusion | Caputo-Fabrizio fractional derivation | Inclusions | Caputo–Fabrizio fractional derivation

MATHEMATICS | MATHEMATICS, APPLIED | Dimension of the set of solutions | Fractional differential inclusion | Caputo-Fabrizio fractional derivation | Inclusions | Caputo–Fabrizio fractional derivation

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 06/2017, Volume 99, pp. 109 - 115

In this article, we analyze the El Nino–Southern Oscillation (ENSO) model in the global climate with a new fractional derivative recently proposed by Caputo...

Caputo–Fabrizio fractional derivative | Fixed point theorem | Atmosphere-ocean | El Nino-Southern Oscillation | Uniqueness | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Caputo-Fabrizio fractional derivative | Models | Numerical analysis | Southern oscillation | Analysis

Caputo–Fabrizio fractional derivative | Fixed point theorem | Atmosphere-ocean | El Nino-Southern Oscillation | Uniqueness | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Caputo-Fabrizio fractional derivative | Models | Numerical analysis | Southern oscillation | Analysis

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2018, Volume 509, pp. 703 - 716

In this paper, we obtain analytical solutions for the fractional cubic isothermal auto-catalytic chemical system with Caputo–Fabrizio and Atangana–Baleanu...

q-HATM | Atangana–Baleanu | [formula omitted]-curves | Fractional isothermal auto-catalytic chemical systems | Caputo–Fabrizio | h-curves | Atangana-Baleanu | LONG-WAVE EQUATION | NUMERICAL-SOLUTION | TRANSPORT | PHYSICS, MULTIDISCIPLINARY | Caputo-Fabrizio | TIME | MODEL | HOMOTOPY ANALYSIS METHOD

q-HATM | Atangana–Baleanu | [formula omitted]-curves | Fractional isothermal auto-catalytic chemical systems | Caputo–Fabrizio | h-curves | Atangana-Baleanu | LONG-WAVE EQUATION | NUMERICAL-SOLUTION | TRANSPORT | PHYSICS, MULTIDISCIPLINARY | Caputo-Fabrizio | TIME | MODEL | HOMOTOPY ANALYSIS METHOD

Journal Article

Acta Mechanica, ISSN 0001-5970, 12/2019, Volume 230, Issue 12, pp. 4367 - 4384

This present work is devoted to the investigation of the transient phenomena for a fiber-reinforced medium with a cylindrical cavity in the context of the...

Engineering | Vibration, Dynamical Systems, Control | Classical and Continuum Physics | Solid Mechanics | Engineering Thermodynamics, Heat and Mass Transfer | Engineering Fluid Dynamics | Theoretical and Applied Mechanics | Fiber reinforced materials | Transport equations | Three phase | Thermoelasticity | Laplace transforms | Phase lag | Magnetic fields

Engineering | Vibration, Dynamical Systems, Control | Classical and Continuum Physics | Solid Mechanics | Engineering Thermodynamics, Heat and Mass Transfer | Engineering Fluid Dynamics | Theoretical and Applied Mechanics | Fiber reinforced materials | Transport equations | Three phase | Thermoelasticity | Laplace transforms | Phase lag | Magnetic fields

Journal Article

Computational and Applied Mathematics, ISSN 0101-8205, 9/2018, Volume 37, Issue 4, pp. 5203 - 5216

In this paper, we extend the model of the Korteweg–de Vries (KDV) and Korteweg–de Vries–Burger’s (KDVB) to new model time fractional Korteweg–de Vries (TFKDV)...

Computational Mathematics and Numerical Analysis | Time fractional Korteweg–de Vries | Mathematics | q-Homotopy analysis transform method | 35-XX | 35Jxx | 35J99 | Atangana–Baleanu | Mathematical Applications in Computer Science | Time fractional Korteweg–de Vries–Burger’s | Liouville–Caputo | Applications of Mathematics | Mathematical Applications in the Physical Sciences | Caputo–Fabrizio

Computational Mathematics and Numerical Analysis | Time fractional Korteweg–de Vries | Mathematics | q-Homotopy analysis transform method | 35-XX | 35Jxx | 35J99 | Atangana–Baleanu | Mathematical Applications in Computer Science | Time fractional Korteweg–de Vries–Burger’s | Liouville–Caputo | Applications of Mathematics | Mathematical Applications in the Physical Sciences | Caputo–Fabrizio

Journal Article

Results in Physics, ISSN 2211-3797, 03/2018, Volume 8, pp. 1061 - 1067

The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated...

Exponentially accelerated plate | Slip | Maxwell fluid | Newtonian heating | Caputo-Fabrizio fractional derivatives | Free convection | Stehfest’s and Tzou’s algorithms | Stehfest's and Tzou's algorithms | exponentially accelerated plate | PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | LIQUID | MODEL | RAYLEIGH-STOKES-PROBLEM | POROUS-MEDIUM | FREE-CONVECTION FLOW | PLATE

Exponentially accelerated plate | Slip | Maxwell fluid | Newtonian heating | Caputo-Fabrizio fractional derivatives | Free convection | Stehfest’s and Tzou’s algorithms | Stehfest's and Tzou's algorithms | exponentially accelerated plate | PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | LIQUID | MODEL | RAYLEIGH-STOKES-PROBLEM | POROUS-MEDIUM | FREE-CONVECTION FLOW | PLATE

Journal Article

Entropy, ISSN 1099-4300, 05/2017, Volume 19, Issue 5, p. 114

In the present paper, we use analytical techniques to solve fractional nonlinear differential equations systems that arise in Bergman’s minimal model, used to...

Mathematical analysis | Differential equations | Uniqueness | Nonlinearity | Systems analysis | Mathematical models | Glucose | Metabolism | Insulin | fractional differential equation | Caputo–Fabrizio fractional derivative | Bergman’s minimal model | Sumudu transform

Mathematical analysis | Differential equations | Uniqueness | Nonlinearity | Systems analysis | Mathematical models | Glucose | Metabolism | Insulin | fractional differential equation | Caputo–Fabrizio fractional derivative | Bergman’s minimal model | Sumudu transform

Journal Article

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