New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model
Abdon Atangana,Dumitru Baleanu +1 more
TLDR
In this article, a new fractional derivative with non-local and no-singular kernel was proposed and applied to solve the fractional heat transfer model, and some useful properties of the new derivative were presented.Abstract:
In this manuscript we proposed a new fractional derivative with non-local and
no-singular kernel. We presented some useful properties of the new derivative
and applied it to solve the fractional heat transfer model.read more
Citations
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Chaos in a simple nonlinear system with Atangana-Baleanu derivatives with fractional order
Abdon Atangana,Ilknur Koca +1 more
TL;DR: In this paper, Atangana and Baleanu proposed a derivative with fractional order to answer some outstanding questions that were posed by many researchers within the field of fractional calculus.
Journal ArticleDOI
A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative
TL;DR: In this paper, a new fractional model for human liver involving Caputo-Fabrizio derivative with the exponential kernel was proposed, and the existence of a unique solution was explored by using the Picard-Lindelof approach and the fixed-point theory.
Journal ArticleDOI
Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system
TL;DR: In this paper, new operators of differentiation have been introduced, such as convolution of power law, exponential decay law, and generalized Mittag-Leffler law with fractal derivative, referred as fractal-fractional differential and integral operators.
Journal ArticleDOI
Decolonisation of fractional calculus rules: Breaking commutativity and associativity to capture more natural phenomena
TL;DR: In this paper, the authors demonstrate the failure of the semi-group principle in modeling real-world problems and demonstrate the importance of non-commutative and non-associative operators under which the Caputo-Fabrizio and Atangana-Baleanu fractional operators fall.
Journal ArticleDOI
Fractal calculus and its geometrical explanation
TL;DR: In this paper, a fractal gradient of temperature is introduced to reveal the basic properties of fractal calculus and the fractal velocity and fractal material derivative are introduced to deduce laws for fluid mechanics and heat conduction in fractal space.
References
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A new Definition of Fractional Derivative without Singular Kernel
Michele Caputo,Mauro Fabrizio +1 more
TL;DR: In this article, the authors present a new definition of fractional derivative with a smooth kernel, which takes on two different representations for the temporal and spatial variable, for which it is more convenient to work with the Fourier transform.
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Application of a fractional advection-dispersion equation
TL;DR: In this article, a transport equation that uses fractional-order dispersion derivatives has fundamental solutions that are Le´vy's a-stable densities, which represent plumesthat spread proportional to time 1/a, have heavy tails, and incorporate any degree of skewness.
Properties of a New Fractional Derivative without Singular Kernel
TL;DR: In this article, the fractional integral corresponding to the new concept of fractional derivative was introduced, and some related fractional differential equations were studied in the context of the FDE.
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On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation
TL;DR: This paper presented useful tools about the new derivative and applied it to the nonlinear Fisher's reaction-diffusion equation and the solution of the modified equation was presented using the notion of iterative method.
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Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels
Michele Caputo,Mauro Fabrizio +1 more
TL;DR: For these new mode ls, the coherence with the thermodynamic laws is proved and the standard linear solid of Zener within continuum mechanics and the model of Cole and Cole inside electromagnetism is revised by these new fractional operators.