COMPARING THE NEW FRACTIONAL DERIVATIVE OPERATORS INVOLVING EXPONENTIAL AND MITTAG-LEFFLER KERNEL
Küçük Resim Yok
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Inst Mathematical Sciences-Aims
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this manuscript, we have proposed a comparison based on newly defined fractional derivative operators which are called as Caputo-Fabrizio (CF) and Atangana-Baleanu (AB). In 2015, Caputo and Fabrizio established a new fractional operator by using exponential kernel. After one year, Atangana and Baleanu recommended a different-type fractional operator that uses the generalized Mittag-Leffler function (MLF). Many real-life problems can be modelled and can be solved by numerical-analytical solution methods which are derived with these operators. In this paper, we suggest an approximate solution method for PDEs of fractional order by using the mentioned operators. We consider the Laplace homotopy transformation method (LHTM) which is the combination of standard homotopy technique (SHT) and Laplace transformation method (LTM). In this study, we aim to demonstrate the effectiveness of the aforementioned method by comparing the solutions we have achieved with the exact solutions. Furthermore, by constructing the error analysis, we test the practicability and usefulness of the method.
Açıklama
Anahtar Kelimeler
Caputo-Fabrizio Fractional Operator, Atangana-Baleanu Fractional Operator, Non-Singular Kernel, Non-Locality, Perturbation Method, Laplace Transformation
Kaynak
Discrete And Continuous Dynamical Systems-Series S
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
13
Sayı
3
