Application of fractional-order Differential Equations on Diffusion and Wave Equations

Authors : Taylan Demir

DOI : 10.13140/RG.2.2.26612.01927

Volume : 1

Issue : 1

Year : 2022

Page No : 1

In this article, I applied many definitions of fractional calculus on physical problems. First of all, I did modelling with diffusion equations and wave equations. Especially, description of transfer proccesses in fractals I. Podlubny [1], B.Mandelbrot [2], A. Le Mehaute, A. de Guibert, M. Delaye and Ch. Filippi [3] was used and suggested of equation in [3] was applied on one-dimension. Second of all, I used generalization of the fractional partial differential equation recommended by K. B. Oldham and J. Spanier with Fick's Law [4]-[5]. Third of all, I metioned that [6]-[7]-[8]-[9]-[10] and [11] to apply on diffusion and wave equations. Finally, I used Matlab on (Sh. Hajrulla, A. Uka, T. Demir, F. Hoxha, D. Hajrulla, L. Bezati [12]) to describe of shallow water wave equations. In briefly, the reason why I was writing this thesis was correlate and did mathematical modelling of definitions of fractional-order differential equations on diffusion and wave equations with respect to time-domain.


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