New idea of Atangana‐Baleanu time‐fractional derivative to advection‐diffusion equation
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DOI: 10.1002/mma.6123
Abstract: The analytical study of one‐dimensional generalized fractional advection‐diffusion equation with a time‐dependent concentration source on the boundary is carried out. The generalization consists into considering the advection‐diffusion equation with memory based on the time‐fractional Atangana‐Baleanu… read more here.
Keywords: advection diffusion; diffusion equation; atangana baleanu; diffusion ... See more keywords
Analysis and numerical computations of the fractional regularized long‐wave equation with damping term
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DOI: 10.1002/mma.6343
Abstract: This study explores the fractional damped generalized regularized long‐wave equation in the sense of Caputo, Atangana‐Baleanu, and Caputo‐Fabrizio fractional derivatives. With the aid of fixed‐point theorem in the Atangana‐Baleanu fractional derivative with Mittag‐Leffler–type kernel, we… read more here.
Keywords: wave equation; long wave; regularized long; atangana baleanu ... See more keywords
Lyapunov functions for fractional‐order nonlinear systems with Atangana–Baleanu derivative of Riemann–Liouville type
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DOI: 10.1002/mma.7690
Abstract: Stability analysis plays an essential role in control systems design. This analysis can be done using different techniques that show the equilibrium points are stable (or unstable). This paper focuses on fractional systems of order… read more here.
Keywords: baleanu derivative; atangana baleanu; derivative riemann; riemann liouville ... See more keywords
On the recurrent computation of fractional operator with Mittag-Leffler kernel
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DOI: 10.1016/j.apnum.2020.12.016
Abstract: Abstract The paper considers the problem of computing the values of the Atangana-Baleanu derivative in Caputo sense which arises while solving fractional partial differential equations. In such case the values of the derivative are needed… read more here.
Keywords: atangana baleanu; leffler function; baleanu derivative; recurrent computation ... See more keywords
A new idea of Atangana-Baleanu time fractional derivatives to blood flow with magnetics particles in a circular cylinder: Two phase flow model
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Magnetism and Magnetic Materials"
DOI: 10.1016/j.jmmm.2019.165282
Abstract: Abstract This study aims to examine the magnetohydrodynamic (MHD) effect on the blood flow of a Casson fluid in a vertical cylinder. Blood is taken as a non-Newtonian viscous fluid due to the viscosity which… read more here.
Keywords: fractional derivatives; magnetics; blood; atangana baleanu ... See more keywords
Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties
Sign Up to like & getrecommendations! Published in 2018 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2018.03.056
Abstract: Abstract We presented an analysis of evolutions equations generated by three fractional derivatives namely the Riemann–Liouville, Caputo–Fabrizio and the Atangana–Baleanu fractional derivatives. For each evolution equation, we presented the exact solution for time variable and… read more here.
Keywords: atangana baleanu; semigroup; time; semigroup principle ... See more keywords
Application of Atangana-Baleanu fractional derivative to convection flow of MHD Maxwell fluid in a porous medium over a vertical plate
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Modelling of Natural Phenomena"
DOI: 10.1051/mmnp/2018007
Abstract: Atangana-Baleanu fractional derivative has been applied to study heat transfer problem of magnetohydrodynamic (MHD) Maxwell fluid over a vertical plate embedded in a porous medium. The analytical solutions have been obtained for temperature distribution and… read more here.
Keywords: atangana baleanu; baleanu fractional; fractional derivative; maxwell ... See more keywords
A fractal-fractional order Atangana-Baleanu model for Hepatitis B virus with asymptomatic class
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DOI: 10.1088/1402-4896/abf67c
Abstract: Hepatitis B is still a major issue in most countries of the world. Due to many death and infection cases, the disease becoming a life-threatening issue and needs proper attention for its eradication. The main… read more here.
Keywords: asymptomatic class; atangana baleanu; hepatitis; model ... See more keywords
Image Denoising of Adaptive Fractional Operator Based on Atangana–Baleanu Derivatives
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DOI: 10.1155/2021/5581944
Abstract: A fractional integral operator can preserve an image edge and texture details as a denoising filter. Recently, a newly defined fractional-order integral, Atangana–Baleanu derivatives (ABC), has been used successfully in image denoising. However, determining the… read more here.
Keywords: atangana baleanu; image; order; baleanu derivatives ... See more keywords
The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators
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DOI: 10.1177/1687814019866540
Abstract: The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new… read more here.
Keywords: caputo fabrizio; atangana baleanu; new chaotic; chaotic system ... See more keywords
Fractional Herglotz variational problems with Atangana–Baleanu fractional derivatives
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Inequalities and Applications"
DOI: 10.1186/s13660-018-1635-9
Abstract: The purpose of this paper is to solve fractional calculus of variational Herglotz problem depending on an Atangana–Baleanu fractional derivative. Since the new Atangana–Baleanu fractional derivative is non-singular and non-local, the Euler–Lagrange equations are proposed… read more here.
Keywords: atangana baleanu; fractional herglotz; fractional derivative; baleanu fractional ... See more keywords