On the new fractional derivative and application to nonlinear Fisher's reaction-diffusion equation

By Abdon Atangana. Applied Mathematics and Computation, 2016

544 citations recorded by the source corpus.

Subfields: Applied Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/05306731025d94d23723b24bf456f5170e2268cb

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In Applied Mathematics

In Control and Systems Engineering

In Modeling and Simulation

Citations in the corpus

New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator (2019, methodology): “Additional applications of the operator are seen in recently published works regarding the analysis of the Korteweg-de Vries-Burgers equation used in liquids and waves dynamics [41], magnetohydrodynamics (MHD) free convection flow of generalized Walters’-B fluid over a static vertical plate [42], an”
Transient heat diffusion with a non-singular fading memory: From the Cattaneo constitutive equation with Jeffrey’s Kernel to the Caputo-Fabrizio time-fractional derivative (2016, background): “The Caputo-Fabrizio time-fractional derivative immediately attracted the interest of the researchers and for about a year after the seminal publication [1] numerous applications have been reported, among them: elasticity [4], resistance and numerical modelling of fractional electric circuit [5, 6], ”
Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, methodology): “For example, FD with respect to the kernel of the exponential function in the sense of the Caputo type was firstly reported in [17-24] and FD with the aid of the kernel of the exponential function in the sense of the Riemann-Liouville type was proposed in [25] and developed in [26].”
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model (2016, background): “We recall that the existing fractional derivatives have been used in many real world problems with great success (see for example Refs.”