Fundamental calculus of the fractional derivative defined with Rabotnov exponential kernel and application to nonlinear dispersive wave model
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Before going further with fractional derivative which is constructed by Rabotnov exponential kernel, there exist many questions that are not addressed. In this paper, we try to recapitulate all the fundamental calculus, which we can obtain with this new fractional operator. The problems in this paper are to determine the solutions of the fractional differential equations where the second members are constant functions, polynomial functions, exponential functions, trigonometric functions, or Mittag-Leffler functions. For all the fractional differential equations, the obtained solutions are represented graphically. The Laplace transform of the fractional derivative with Rabotnov exponential kernel is the primary tool in the investigations. Finally, we give the fundamental solution to the nonlinear time-fractional modified Degasperis-Procesi equation by considering the fractional operator with Rabotnov exponential kernel. (c) 2020 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
Açıklama
Anahtar Kelimeler
Fractional Differential Equation, Nonlinear Dispersive Wave Model, Rabotnov Exponential Kernel, Mittag-Leffler Function, Laplace Transformation
Kaynak
Journal Of Ocean Engineering And Science
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
6
Sayı
2
