Korteweg-De Vries-Burgers (KDVB) equation with Atangana-Baleanu derivative with fractional order

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DOKUYUCU M. A.

Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, vol.10, no.3, pp.727-733, 2020 (ESCI)

• Publication Type: Article / Article
• Volume: 10 Issue: 3
• Publication Date: 2020
• Journal Name: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
• Page Numbers: pp.727-733
• Ondokuz Mayıs University Affiliated: No

Abstract

In this work, we examine the Korteweg-de Vries-Burgers equation with two perturbation's levels to the concepts of fractional differentiation with no singularity. The Korteweg-de Vries-Burgers equation was constructed using the new fractional differentiation based on the generalized Mittag-Leffler function due to the non-locality. It is presented the existence of a positive set of the solutions for the KDVB equation. The uniqueness of the positive solutions was presented in detail.