Abstract
In this paper we investigate anomalous diffusion coupled with linear convection, using fractional calculus to describe the anomalous associated memory effects in diffusive term. We get an explicit travelling wave solution, wavefront, with finite propagation. We comment the properties of the solution, including the stationary case.
Highlights
In this paper we investigate anomalous diffusion coupled with linear convection, using fractional calculus to describe the anomalous associated memory effects in diffusive term
We study the diffusion with linear convection, that is, a nonlinear convection-diffusion problem
We are interested in travelling wave solution given by similarity reductions to fractional equation
Summary
The Riesz fractional derivative of order α , with 0 < α < 2 and α ≠ 1 is defined by: Dxα f (x) =. Where D±α f ( x) are Weyl fractional derivatives [20] [21]. Let be h ( x) = x −α −1 , with 1 < α < 2. We describe the Riesz fractional derivative of order α for an appropriate Fourier convolution product is given by: Dxα f= ( x) dα ( f ∗ h)( x),. This result is an improvement of the theorem developed by E. C. de Oliveira [22]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
