A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL Application to the Modelling of the Steady Heat Flow

By Xiao-jun Yang, Hari M. Srivastava, J. Machado. 2015

241 citations recorded by the source corpus.

In this article we propose a new fractional derivative without singular kernel. We consider the potential application for modeling the steady heat-conduction problem. The analytical solution of the fractional-order heat flow is also obtained by means of the Laplace transform.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7cc6752927f67764387fa5163ce2d2fa7ad290aa

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In Mechanics of Materials

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Iterative methods for solving fourth‐ and sixth‐order time‐fractional Cahn‐Hillard equation (2019, background): “Considering Equations (9) to (13), from Equation (8), we have”
Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, methodology): “Recently, FDs involving the kernels of the exponential and Mittag-Leffler functions were reported in [17,18,19,20,21,22,23,24].”
On a differential equation with Caputo-Fabrizio fractional derivative of order $1<\beta\leq 2$ and application to mass-spring-damper system (2016, methodology): “Namely, in [6], application to nonlinear Fisher’s reaction-diffusion equation, in [7], application to steady heat flow, in [8], application to Korteweg-de Vries-Bergers equation, in [9], [10], application to groundwater flow and in [11], application to the studying chaos on the Vallis model for El N”
A new fractional operator of variable order: Application in the description of anomalous diffusion (2016, methodology): “POD using the function kernel of the exponential type were reported in [12,13,14,15].”